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Handbook of Group Actions（群作用手册）（第II卷）

样章
作者：
季理真, Papadopoulos, 丘成桐
定价：
128.00元
ISBN：
978-7-04-041389-2
版面字数：
950千字
开本：
16开
全书页数：
573页
装帧形式：
精装
重点项目：
暂无
出版时间：
2014-12-31
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

群和群作用是数学研究的重要对象，拥有强大的 力量并且富于美感，这可以通过它广泛出现在诸多不 同的科学领域体现出来。

《群作用手册》由相关领域专家撰写的一系列综 述文章组成，首次系统地展现了群作用及其应用，内 容囊括经典主题的讨论、近来的热点专业问题的论述 ，有些文章还涉及相关的历史。本书填补了数学著作 中的一项空白，适合于从初学者到相关领域专家的各 个层次读者阅读。

  • 前辅文
  • Part I: Geometric Topology
    • Exotic Topology in Geometry and Dynamics
    • F. Thomas Farrell, Andrey Gogolev, and Pedro Ontaneda
      • 1 The space of negatively curvedmetrics
      • 2 The Teichm¨uller and the moduli spaces of negatively curved metrics
      • 3 Bundles with negatively curved fibers
      • 4 Exotic topology and hyperbolic dynamical systems
      • References
    • A Survey of Surface Braid Groups and the Lower Algebraic K-Theory of Their Group Rings
    • John Guaschi and Daniel Juan-Pineda
      • 1 Introduction
      • 2 Basic definitions of surface braid groups
      • 3 Some properties of surface braid groups
      • 4 Braid groups of the sphere and the projective plane
      • 5 K-theory of surface braid groups
      • Acknowledgments
      • References
    • The Isomorphism Conjecture for Groups with Generalized Free Product Structure
    • Sayed K. Roushon
      • 1 Introduction
      • 2 LowerK-theory and surgery L-theory of groups acting on trees 3
      • 3 The isomorphism conjecture for groups acting on trees
      • Acknowledgments
      • References
    • Group Actions on Banach Spaces
    • Piotr W. Nowak
      • 1 Introduction
      • 2 Preliminaries
      • 3 Fixed points
      • 4 Metrically proper actions
      • 5 Final remarks
      • Acknowledgments
      • References
    • Topological Spherical Space Forms
    • Ian Hambleton
      • 1 Introduction
      • 2 First steps: pre-1960
      • 3 Swan complexes: 1960–1970
      • 4 Semicharacteristic obstructions and 3-manifolds
      • 5 Poincar´e complexes
      • 6 Surgery theory and stable existence
      • 7 The finiteness obstruction
      • 8 Space forms in the period dimension
      • 9 Topological Euclidean space forms
      • 10 Further topics
      • References
  • Part II: Representations and Deformations
    • Dynamics on Character Varieties: A Survey.
    • Richard D. Canary
      • 1 Overview
      • 2 Basic definitions
      • 3 Teichm¨uller space
      • 4 Convex cocompact representations
      • 5 Hitchin representations
      • 6 Anosov representations
      • 7 PSL(2,C)-character varieties
      • 8 Appendix
      • References
    • Higgs Bundles and Representations of Complex Hyperbolic Lattices
    • Julien Maubon
      • 1 Introduction
      • 2 The symmetric space SU(p, q)/S(U(p) × U(q))
      • 3 Representations, flat bundles, Higgs bundles
      • 4 Proof of the Milnor-Wood type inequality
      • 5 Maximal representations
      • References
    • Geometric Limits of Kleinian Groups and Their Applications
    • Ken’ichi Ohshika
      • 1 Introduction
      • 2 Preliminaries
      • 3 Examples of geometric limits
      • 4 Classification of geometric limits
      • 5 Boundaries of deformation spaces
      • References
    • Deformations of Surfaces Embedded in 4-dimensional Manifolds and Their Mapping Class Groups
    • Susumu Hirose
      • 1 Introduction
      • 2 Preliminaries
      • 3 Surfaces standardly embedded in S4
      • 4 Flexible surfaces in 4-manifolds
      • 5 Knotted embeddings in S4
      • 6 Problems
      • Acknowledgments
      • References
    • On the Geography of Lefschetz Fibrations
    • Naoyuki Monden
      • 1 Introduction
      • 2 Lefschetz fibrations
      • 3 Examples of Lefschetz fibrations
      • 4 Signatures of Lefschetz fibrations
      • 5 Fundamental groups of Lefschetz fibrations
      • 6 Some methods to construct Lefschetz fibrations
      • 7 Sections of Lefschetz fibrations
      • 8 The geography problems of symplectic 4-manifolds and Lefschetz fibrations
      • 9 Holomorphic and non-holomorphic Lefschetz fibrations
      • 10 The slopes of Lefschetz fibrations with b+2 =1
      • Acknowledgments
      • References
  • Part III: Geometric Groups
    • The Modular Group and Its Actions.
    • A. Muhammed Uluda˘g
      • 1 Introduction
      • 2 Rise of the modular group
      • 3 The bipartite Farey tree F and its boundary
      • 4 The projective general linear group over Z
      • 5 Action on the upper half plane H
      • 6 Modular graphs and dessins
      • 7 The action on binary quadratic forms
      • 8 Et cetera
      • Appendix: Gosper’s algorithm for continued fraction arithmetic
      • Acknowledgments
      • References
    • Groups with Structures and Homotopy Groups
    • Jie Wu
      • 1 Introduction
      • 2 Simplicial groups
      • 3 Simplicial structure on geometric groups
      • Acknowledgments
      • Contents V
      • References
    • Abstract Homomorphisms of Algebraic Groups and Applications
    • Igor A. Rapinchuk
      • 1 Introduction
      • 2 On algebraic rings
      • 3 K-theoretic background
      • 4 Rigidity results over commutative rings
      • 5 Rigidity results over noncommutative rings
      • 6 Applications to character varieties and deformations of
      • representations
      • Acknowledgments
      • References
  • Part IV: Geometric Invariants and Growth of Discrete Groups
    • Some Topics in Geometric Invariant Theory over Non-algebraically Closed Fields
    • D`ao Phuong Bˇa´c and Nguyˆe˜n Quˆo´c Thˇa´ng
      • 1 Introduction
      • 2 An overview of geometric invariant theory. Observability and
      • related notions
      • 3 Stability in geometric invariant theory over non-algebraically
      • closed fields
      • 4 Topology of relative orbits for actions of algebraic groups over
      • completely valued fields
      • Acknowledgments
      • References
    • Computation of the Spherical Growth Series of Finitely Generated Groups and Monoids by Using Automata Michihiko Fujii
      • 1 Introduction
      • 2 Finite-state automata and the subset construction
      • 3 Unique-geodesic word acceptors for groups and monoids, and growth series
      • 4 Examples of rational growth series and irrational growth series
      • 5 The spherical growth series of Artin groups and Artin monoids
      • 6 The pure Artin group PI2(k) and the monoid P+I2(k) of dihedraltype
      • 7 Automata for geodesic representatives of P+I2(k)
      • 8 Unique-geodesic word acceptors constructed by subset construction
      • 9 The spherical growth series of P+I2(k)
      • 10 The spherical growth series of PI2(k)
      • Acknowledgments
      • References
  • Part V: Music and Group Actions
    • Mathematics and Group Theory in Music
    • Athanase Papadopoulos
      • 1 Introduction
      • 2 A brief overview of the interaction between mathematics
      • and music
      • 3 The music of OlivierMessiaen
      • 4 Rhythm
      • 5 Counterpoint
      • 6 Modes of limited transposition
      • References

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