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几何群论（影印版）

样章
作者：
Mladen Bestvina，Michah Sageev，Karen Vogtmann 编
定价：
169.00元
ISBN：
978-7-04-059310-5
版面字数：
700.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2023-03-23
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：
几何学
暂无
  • 前辅文
  • Mladen Bestvina, Michah Sageev, Karen Vogtmann Introduction
  • Michah Sageev CAT(0) Cube Complexes and Groups
    • Introduction
    • Lecture 1. CAT(0) cube complexes and pocsets
      • 1. The basics of NPC and CAT(0) complexes
      • 2. Hyperplanes
      • 3. The pocset structure
    • Lecture 2. Cubulations: from pocsets to CAT(0) cube complexes
      • 1. Ultrafilters
      • 2. Constructing the complex from a pocset
      • 3. Examples of cubulations
      • 4. Cocompactness and properness
      • 5. Roller duality
    • Lecture 3. Rank rigidity
      • 1. Essential cores
      • 2. Skewering
      • 3. Single skewering
      • 4. Flipping
      • 5. Double skewering
      • 6. Hyperplanes in sectors
      • 7. Proving rank rigidity
    • Lecture 4. Special cube complexes
      • 1. Subgroup separability
      • 2. Warmup - Stallings’ proof of Marshall Hall’s theorem
      • 3. Special cube complexes
      • 4. Canonical completion and retraction
      • 5. Application: separability of quasiconvex subgroups
      • 6. Hyperbolic cube complexes are virtually special
    • Bibliography
  • Vincent Guirardel Geometric Small Cancellation
    • Introduction
    • Lecture 1. What is small cancellation about?
      • 1. The basic setting
      • 2. Applications of small cancellation
      • 3. Geometric small cancellation
    • Lecture 2. Applying the small cancellation theorem
      • 1. When the theorem does not apply
      • 2. Weak proper discontinuity
      • 3. SQ-universality
      • 4. Dehn fillings
    • Lecture 3. Rotating families
      • 1. Road-map of the proof of the small cancellation theorem
      • 2. Definitions
      • 3. Statements
      • 4. Proof of Theorem 3.4
      • 5. Hyperbolicity of the quotient
      • 6. Exercises
    • Lecture 4. The cone-off
      • 1. Presentation
      • 2. The hyperbolic cone of a graph
      • 3. Cone-off of a space over a family of subspaces
    • Bibliography
  • Pierre-Emmanuel Caprace Lectures on Proper CAT(0) Spaces and Their Isometry Groups
    • Introduction
    • Lecture 1. Leading examples
      • 1. The basics
      • 2. The Cartan–Hadamard theorem
      • 3. Proper cocompact spaces
      • 4. Symmetric spaces
      • 5. Euclidean buildings
      • 6. Rigidity
      • 7. Exercises
    • Lecture 2. Geometric density
      • 1. A geometric relative of Zariski density
      • 2. The visual boundary
      • 3. Convexity
      • 4. A product decomposition theorem
      • 5. Geometric density of normal subgroups
      • 6. Exercises
    • Lecture 3. The full isometry group
      • 1. Locally compact groups
      • 2. The isometry group of an irreducible space
      • 3. de Rham decomposition
      • 4. Exercises
    • Lecture 4. Lattices
      • 1. Geometric Borel density
      • 2. Fixed points at infinity
      • 3. Boundary points with a cocompact stabiliser
      • 4. Back to rigidity
      • 5. Flats and free abelian subgroups
      • 6. Exercises
    • Bibliography
  • Michael Kapovich Lectures on Quasi-Isometric Rigidity
    • Introduction: What is Geometric Group Theory?
    • Lecture 1. Groups and spaces
      • 1. Cayley graphs and other metric spaces
      • 2. Quasi-isometries
      • 3. Virtual isomorphisms and QI rigidity problem
      • 4. Examples and non-examples of QI rigidity
    • Lecture 2. Ultralimits and Morse lemma
      • 1. Ultralimits of sequences in topological spaces
      • 2. Ultralimits of sequences of metric spaces
      • 3. Ultralimits and CAT(0) metric spaces
      • 4. Asymptotic cones
      • 5. Quasi-isometries and asymptotic cones
      • 6. Morse lemma
    • Lecture 3. Boundary extension and quasi-conformal maps
      • 1. Boundary extension of QI maps of hyperbolic spaces
      • 2. Quasi-actions
      • 3. Conical limit points of quasi-actions
      • 4. Quasiconformality of the boundary extension
    • Lecture 4. Quasiconformal groups and Tukia’s rigidity theorem
      • 1. Quasiconformal groups
      • 2. Invariant measurable conformal structure for qc groups
      • 3. Proof of Tukia’s theorem
      • 4. QI rigidity for surface groups
    • Appendix.
      • 1. Hyperbolic space
      • 2. Least volume ellipsoids
      • 3. Different measures of quasiconformality
    • Bibliography
  • Mladen Bestvina Geometry of Outer Space
    • Introduction
    • Lecture 1. Outer space and its topology
      • 1.1. Markings
      • 1.2. Metric
      • 1.3. Lengths of loops
      • 1.4. Fn-trees
      • 1.5. Topology and Action
      • 1.6. Thick part and spine
      • 1.7. Action of Out(Fn)
      • 1.8. Rank 2 picture
      • 1.9. Contractibility
      • 1.10. Group theoretic consequences
    • Lecture 2. Lipschitz metric, train tracks
      • 2.1. Definitions
      • 2.2. Elementary facts
      • 2.3. Example
      • 2.4. Tension graph, train track structure
      • 2.5. Folding paths
    • Lecture 3. Classification of automorphisms
      • 3.1. Elliptic automorphisms
      • 3.2. Hyperbolic automorphisms
      • 3.3. Parabolic automorphisms
      • 3.4. Reducible automorphisms
      • 3.5. Growth
      • 3.6. Pathologies
    • Lecture 4. Hyperbolic features
      • 4.1. Complex of free factors Fn
      • 4.2. The complex Sn of free factorizations
      • 4.3. Coarse projections
      • 4.4. Idea of the proof of hyperbolicity
    • Bibliography
  • Dave Witte Morris Some Arithmetic Groups that Do Not Act on the Circle
    • Abstract
    • Lecture 1. Left-orderable groups and a proof for SL(3, Z)
      • 1A. Introduction
      • 1B. Examples
      • 1C. The main conjecture
      • 1D. Left-invariant total orders
      • 1E. SL(3, Z) does not act on the line
      • 1F. Comments on other arithmetic groups
    • Lecture 2. Bounded generation and a proof for SL(2, Z[α])
      • 2A. What is bounded generation?
      • 2B. Bounded generation of SL(2, Z[α])
      • 2C. Bounded orbits and a proof for SL(2, Z[α])
      • 2D. Implications for other arithmetic groups of higher rank
    • Lecture 3. What is an amenable group?
      • 3A. Ponzi schemes
      • 3B. Almost-invariant subsets
      • 3C. Average values and invariant measures
      • 3D. Examples of amenable groups
      • 3E. Applications to actions on the circle
    • Lecture 4. Introduction to bounded cohomology
      • 4A. Definition
      • 4B. Application to actions on the circle
      • 4C. Computing H2 b (Γ
    • Appendix. Hints for the exercises
    • Bibliography
  • Tsachik Gelander Lectures on Lattices and Locally Symmetric Spaces
    • Introduction
    • Lecture 1. A brief overview on the theory of lattices
      • 1. Few definitions and examples
      • 2. Lattices resemble their ambient group in many ways
      • 3. Some basic properties of lattices
      • 4. A theorem of Mostow about lattices in solvable groups
      • 5. Existence of lattices
      • 6. Arithmeticity
    • Lecture 2. On the Jordan–Zassenhaus–Kazhdan–Margulis theorem
      • 1. Zassenhaus neighborhood
      • 2. Jordan’s theorem
      • 3. Approximations by finite transitive spaces
      • 4. Margulis’ lemma
      • 5. Crystallographic manifolds
    • Lecture 3. On the geometry of locally symmetric spaces and some
    • finiteness theorems
      • 1. Hyperbolic spaces
      • 2. The thick–thin decomposition
      • 3. Presentations of torsion free lattices
      • 4. General symmetric spaces
      • 5. Number of generators of lattices
    • Lecture 4. Rigidity and applications
      • 1. Local rigidity
      • 2. Wang’s finiteness theorem
      • 3. Mostow’s rigidity theorem
      • 4. Superrigidity and arithmeticity
      • 5. Invariant random subgroups and the Nevo–Stuck–Zimmer theorem
    • Bibliography
  • Amie Wilkinson Lectures on Marked Length Spectrum Rigidity
    • Introduction
    • Lecture 1. Preliminaries
      • 1. Background on negatively curved surfaces
      • 2. A key example
      • 3. Geodesics in negative curvature
      • 4. The geodesic flow
    • Lecture 2. Geometry and dynamics in negative curvature
      • 1. Busemann functions and horospheres
      • 2. The space of geodesics and the boundary at infinity
      • 3. The Liouville current, the cross ratio and the canonical contact form
      • 4. Summary: a dictionary
    • Lecture 3. The proof, Part I: A volume preserving conjugacy
      • 1. Otal’s Proof
    • Lecture 4. The proof, Part II: Volume preserving implies isometry
    • Final Comments
    • Bibliography
  • Emmanuel Breuillard Expander Graphs, Property (τ ) and Approximate Groups
    • Foreword
    • Lecture 1. Amenability and random walks
      • A. Amenability, Folner criterion
      • B. Isoperimetric inequality, edge expansion
      • C. Invariant means
      • D. Random walks on groups, the spectral radius and Kesten’s criterion
      • E. Further facts and questions about growth of groups and random walks
      • F. Exercise: Paradoxical decompositions, Ponzi schemes and Tarski numbers
    • Lecture 2. The Tits alternative and Kazhdan’s property (T)
      • A. The Tits alternative
      • B. Kazhdan’s property (T)
      • C. Uniformity issues in the Tits alternative, non-amenability and Kazhdan’s property (T)
    • Lecture 3. Property (τ ) and expanders
      • A. Expander graphs
      • B. Property (τ )
    • Lecture 4. Approximate groups and the Bourgain-Gamburd method
      • A. Which finite groups can be turned into expanders?
      • B. The Bourgain-Gamburd method
      • C. Approximate groups
      • D. Random generators and the uniformity conjecture
      • E. Super-strong approximation
    • Appendix. The Brooks-Burger transfer
    • Bibliography
  • Martin R. Bridson Cube Complexes, Subgroups of Mapping Class Groups, and Nilpotent Genus
    • 1. Introduction
    • 2. Subgroups of mapping class groups
    • 3. Fibre products and subdirect products of free groups
    • 4. A new level of complication
    • 5. The nilpotent genus of a group
    • 6. Cubes, RAAGs and CAT(0)
    • 7. Rips, fibre products and 1-2-3
    • 8. Examples template
    • 9. Proofs from the template
    • 10. The isomorphism problem for subgroups of RAAGs and Mod(S)
    • 11. Dehn functions
    • Bibliography

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