图书信息
图书目录
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
暂无简介
作者：
季理真、黎景辉、梁志斌、周国晖
定价：
99.00元
出版时间：
2024-11-18
ISBN：
978-7-04-062874-6
物料号：
62874-00
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
重点项目：
暂无
版面字数：
360.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
平装
- 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
- 1.1 Geometry
- 2. Chevalley Groups
- 2.1 (B
- 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
- 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
- 1. Combinatorics
- 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
- 5. Introduction and History of Buildings
- Index
