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楼理论及其在几何和拓扑中的应用（Theory of Buildings and Applications in Geometry and Topology）（英

样章
作者：
季理真、黎景辉、梁志斌、周国晖
定价：
99.00 元
版面字数：
360千字
开本：
特殊
装帧形式：
平装
版次：
1
最新版次
印刷时间：
2024年
ISBN：
978-7-04-062874-6
物料号：
62874-00
出版时间：
2024-11-18
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
代数学
暂无
  • 目录
    • 前辅文
      • Part 1 Buildings and Groups
        • 1. Combinatorics
          • 1.1 Geometry
            • 1.1.1 Graphs
              • 1.1.2 Trees
                • 1.1.3 Euclidean geometry
                  • 1.1.4 Incidence geometry
                    • 1.1.5 Projective space
                    • 1.2 Coxeter group
                      • 1.2.1 Coxeter system
                        • 1.2.2 Finite reflection group
                          • 1.2.3 Affine reflection group
                          • 1.3 Chamber systems
                            • 1.3.1 Edge-colored graphs
                              • 1.3.2 Buildings
                              • 1.4 Chamber complexes
                                • 1.4.1 Complexes
                                  • 1.4.2 Chamber complex
                                    • 1.4.3 Building
                                    • 1.5 Conclusion
                                    • 2. Chevalley Groups
                                      • 2.1 (B;N) pairs
                                        • 2.2 Simple Lie algebras
                                          • 2.2.1 An
                                            • 2.2.2 Bn
                                              • 2.2.3 Cn
                                                • 2.2.4 Dn
                                                • 2.3 Classical groups
                                                  • 2.3.1 GLn
                                                    • 2.3.2 SLn
                                                      • 2.3.3 Sp2n
                                                        • 2.3.4 SO2n
                                                          • 2.3.5 SO2n+
                                                          • 2.4 Chevalley groups and (B;N) pairs
                                                            • 2.4.1 Chevalley basis
                                                              • 2.4.2 Lie algebra representations
                                                                • 2.4.3 Building of a Chevalley group
                                                                  • 2.4.4 SLn
                                                                  • 2.5 Chevalley groups over local fields
                                                                    • 2.5.1 Affine roots
                                                                      • 2.5.2 BN pair
                                                                      • 2.6 Examples
                                                                        • 2.6.1 Sp
                                                                          • 2.6.2 SLn
                                                                            • 2.6.3 SL3(Qp)
                                                                              • 2.6.4 SL2(Qp)
                                                                              • 2.7 Conclusion
                                                                              • 3. Reductive Groups over Local Fields
                                                                                • 3.1 Root data
                                                                                  • 3.2 Reductive group
                                                                                    • 3.2.1 Roots
                                                                                      • 3.2.2 Root data
                                                                                        • 3.2.3 Root group data
                                                                                          • 3.2.4 Pinning
                                                                                          • 3.3 Apartments
                                                                                            • 3.3.1 Affine space
                                                                                              • 3.3.2 Affine apartment
                                                                                                • 3.3.3 Affine extension
                                                                                                  • 3.3.4 Affine roots
                                                                                                  • 3.4 Building of a reductive group
                                                                                                    • 3.4.1 Quasi-split groups
                                                                                                      • 3.4.2 Filtration on root groups
                                                                                                        • 3.4.3 Construction of the building
                                                                                                        • 3.5 Compactification of buildings
                                                                                                          • 3.5.1 Compactifying apartments
                                                                                                            • 3.5.2 Metric
                                                                                                              • 3.5.3 X
                                                                                                              • 3.6 Congruence subgroup
                                                                                                                • 3.6.1 Models
                                                                                                                  • 3.6.2 Smooth models of root subgroups
                                                                                                                    • 3.6.3 Filtrations on tori
                                                                                                                      • 3.6.4 Smooth models associated to concave functions
                                                                                                                      • 3.7 Bounded subgroups
                                                                                                                        • 3.7.1 Maximal bounded subgroups
                                                                                                                          • 3.7.2 Parabolics
                                                                                                                            • 3.7.3 Decompositions
                                                                                                                            • 3.8 Hecke algebra
                                                                                                                              • 3.8.1 Hecke algebra as a matrix algebra
                                                                                                                                • 3.8.2 Hecke algebra of p-adic groups
                                                                                                                                  • 3.8.3 Iwahori subgroup and buildings
                                                                                                                                    • 3.8.4 Iwahori-Hecke algebra
                                                                                                                                      • 3.8.5 Hecke algebra and Coxeter group
                                                                                                                                      • 3.9 Sheaves on buildings
                                                                                                                                        • 3.9.1 Coefficient systems
                                                                                                                                          • 3.9.2 Sheaves
                                                                                                                                        • 4. Rigid Analytic Spaces
                                                                                                                                          • 4.1 Rigid analytic space and formal schemes
                                                                                                                                            • 4.2 Theorems of Mumford and Drinfeld
                                                                                                                                              • 4.2.1 Uniformization
                                                                                                                                                • 4.2.2 Moduli problem
                                                                                                                                                • 4.3 Geometric invariant theory
                                                                                                                                                  • 4.3.1 Stable points
                                                                                                                                                    • 4.3.2 Toric action
                                                                                                                                                    • 4.4 Mumford prolongation
                                                                                                                                                      • 4.5 Formal schemes from flag varieties
                                                                                                                                                        • 4.6 Analytic generic fiber
                                                                                                                                                        • Bibliography
                                                                                                                                                        • Part 2 Buildings and Their Applications in Geometry and Topology
                                                                                                                                                          • 5. Introduction and History of Buildings
                                                                                                                                                            • 5.1 Summary
                                                                                                                                                              • 5.2 History of buildings and outline of this part
                                                                                                                                                                • 5.3 Acknowledgments and dedication
                                                                                                                                                                • 6. Spherical Tits Buildings
                                                                                                                                                                  • 6.1 Definition of buildings as chamber complexes and Solomon-Tits theorem
                                                                                                                                                                    • 6.2 Semisimple Lie groups and buildings
                                                                                                                                                                      • 6.3 BN-pairs or Tits systems, and buildings
                                                                                                                                                                        • 6.4 Other definitions of and approaches to buildings
                                                                                                                                                                          • 6.5 Rigidity of Tits buildings
                                                                                                                                                                          • 7. Geometric Realizations and Applications of Spherical Tits Buildings
                                                                                                                                                                            • 7.1 Geodesic compactification of symmetric spaces
                                                                                                                                                                              • 7.2 Buildings and compactifications of symmetric spaces
                                                                                                                                                                                • 7.3 Topological spherical Tits buildings and Moufang buildings
                                                                                                                                                                                  • 7.4 Mostow strong rigidity
                                                                                                                                                                                    • 7.5 Rank rigidity of manifolds of nonpositive curvature
                                                                                                                                                                                      • 7.6 Rank rigidity for CAT(0)-spaces and CAT(0)-groups
                                                                                                                                                                                        • 7.7 Classification of isoparametric submanifolds
                                                                                                                                                                                          • 7.8 Spherical buildings and compactifications of locally symmetric spaces
                                                                                                                                                                                            • 7.9 Geodesic compactification, Gromov compactification and large scale geometry
                                                                                                                                                                                              • 7.10 Cohomology of arithmetic groups
                                                                                                                                                                                                • 7.11 Vanishing of simplicial volume of high rank locally symmetric spaces
                                                                                                                                                                                                  • 7.12 Generalizations of buildings: curve complexes and applications
                                                                                                                                                                                                  • 8. Euclidean Buildings
                                                                                                                                                                                                    • 8.1 Definitions and basic properties
                                                                                                                                                                                                      • 8.2 Semisimple p-adic groups and Euclidean buildings
                                                                                                                                                                                                        • 8.3 Compactification of Euclidean buildings by spherical buildings
                                                                                                                                                                                                          • 8.4 Satake compactifications of Bruhat-Tits buildings
                                                                                                                                                                                                          • 9. Applications of Euclidean Buildings
                                                                                                                                                                                                            • 9.1 p-adic curvature and vanishing of cohomology of lattices
                                                                                                                                                                                                              • 9.2 Super-rigidity and harmonic maps into Euclidean buildings
                                                                                                                                                                                                                • 9.3 Applications to S-arithmetic groups
                                                                                                                                                                                                                  • 9.4 Applications to harmonic analysis and representation theories
                                                                                                                                                                                                                  • 10. R-trees and R-buildings
                                                                                                                                                                                                                    • 10.1 Definition of R-trees and basic properties
                                                                                                                                                                                                                      • 10.2 Applications of R-trees in topology
                                                                                                                                                                                                                        • 10.3 R-Euclidean buildings
                                                                                                                                                                                                                          • 10.4 Quasi-isometry rigidity and tangent cones at infinity of symmetric spaces
                                                                                                                                                                                                                          • 11. Twin Buildings and Kac-Moody Groups
                                                                                                                                                                                                                            • 11.1 Twin buildings
                                                                                                                                                                                                                              • 11.2 Kac-Moody algebras and Kac-Moody groups
                                                                                                                                                                                                                                • 11.3 Kac-Moody groups as lattices and groups arising from buildings in geometric group theory
                                                                                                                                                                                                                                • 12. Other Applications of Buildings
                                                                                                                                                                                                                                  • 12.1 Applications in algebraic geometry
                                                                                                                                                                                                                                    • 12.2 Random walks and the Martin boundary
                                                                                                                                                                                                                                      • 12.3 Finite groups
                                                                                                                                                                                                                                        • 12.4 Finite geometry
                                                                                                                                                                                                                                          • 12.5 Algebraic K-groups
                                                                                                                                                                                                                                            • 12.6 Algebraic combinatorics
                                                                                                                                                                                                                                              • 12.7 Expanders and Ramanujan graphs
                                                                                                                                                                                                                                              • Bibliography
                                                                                                                                                                                                                                              • Index

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