组合代数拓扑 本书特色
Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject ibook form. The first part of the book constitutes a swft walk through the maitools of algebraic topology，including Stiefel-Whitney characteristic classes，which are needed for the later. parts. Readers-graduate students and working mathematicians alike-will probably find particularly useful the second part，which contains ain-depth discussioof the major research techniques of combinatorial algebraic topology. Our presentatioof standard topics is quite different from that of existing texts. Iaddition， several new themes，such as spectral sequences，are included. Although applications are sprinkled throughout the second part，they are principal focus of the third part，which is entirely devoted to developing the topological structure theory for graph homomorphisms. The maibenefit for the reader will be the prospect of fairly quickly getting to the forefront of modem research ithis active field.
组合代数拓扑 内容简介
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组合代数拓扑 目录
1 Overture
Part Ⅰ Concepts of Algebraic Topology
2 Cell Complexes
2．1 Abstract Simplicial Complexes
2．1．1 Definitioof Abstract Simplicial Complexes and Maps BetweeThem
2．1．2 Deletion，Link，Star，and Wedge
2．1．3 Simplicial Join
2．1．4 Face Posets
2．1．5 Barycentric and Stellar Subdivisions
2．1．6 Pulling and Pushing Simplicial Structures
2．2 Polyhedral Complexes
2．2．1 Geometry of Abstract Simplicial Complexes
2．2．2 Geometric Meaning of the Combinatorial Constructions
2．2．3 Geometric Simplicial Complexes
2．2．4 Complexes Whose Cells Belong to a Specified Set of Polyhedra
2．3 Trisps
2．3．1 ConstructioUsing the Gluing Data
2．3．2 Constructions Involving Trisps
2．4 CW Complexes
2．4．1 Gluing Along a Map
2．4．2 Constructive and Intrinsic Definitions
2．4．3 Properties and Examples
3 Homology Groups
3．1 Betti Numbers of Finite Abstract Simplicial Complexes
3．2 Simplicial Homology Groups
X Contents
3．2．1 Homology Groups of Trisps with Coefficients iZ2
3．2．2 Orientations
3．2．3 Homology Groups of Trisps with Integer Coefficients
3．3 Invariants Connected to Homology Groups
3．3．1 Betti Numbers and TorsioCoefficients
3．3．2 Euler Characteristic and the Euler-Poincar6 Fc'rmula
3．4 Variations
3．4．1 Augmentatioand Reduced Homology Groups
3．4．2 Homology Groups with Other Coefficients
3．4．3 Simplicial Cohomology Groups
3．4．4 Singular Homology
3．5 ChaiComplexes
3．5．1 Definitioand Homology of ChaiComplexes
3．5．2 Maps BetweeChaiComplexes and Induced MapsoHomology
3．5．3 ChaiHomotopy
3．5．4 Simplicial Homology and Cohomology ithe Contextof ChaiComplexes
3．5．5 Homomorphisms oHomology Induced by Trisp Maps
3．6 Cellular Homology
3．6．1 AApplicatioof Homology with Integer Coefficients：Winding Number
3．6．2 The Definitioof Cellular Homology
3．6．3 Cellular Maps and Properties of Cellular Homology
4 Concepts of Category Theory
4．1 The Notioof a Category
4．1．1 Definitioof a Category．Isomorphisms
4．1．2 Examples of Categories
4．2 Some Structure Theory of Categories
4．2．1 Initial and Terminal Objects
4．2．2 Products and Coproducts
4．3 Functors
4．3．1 The Category Cat
4．3．2 Homology and Cohomology Viewed as Functors
4．3．3 Group Actions as Functors
4．4 Limit C0nstructions
4．4．1 Definitioof Colimit of a Functor
4．4．2 Colimits and Infinite Unions
4．4．3 Quotients of Group Actions as Colimits
4．4．4 Limits
4．5 Comma Categories
4．5．1 Objects Below and Above Other Objects
4．5．2 The General Constructioand Further Examples
……
Part Ⅱ Methods of Combinatorial Algebraic Topology
Part Ⅲ Complexes of Graph Homomorphisms
References
Index
