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