- 代数拓扑简明教程(第2卷)(英文版)
- - 作者：(美)乔·彼得·梅//凯思琳·庞托
  - 出版社：世界图书出版公司
  - ISBN：9787519266424
  - 出版日期：2019/09/01
  - 页数：514
- 售价：31.6

内容大纲
《代数拓扑简明教程（第1卷）》里包含了代数拓扑学的入门知识，如基本群、覆叠空间、同伦、同调和上同调等，这本《代数拓扑简明教程（第2卷）》里则介绍了更多标准代数拓扑教科书通常没有提及的重要内容，如拓扑空间的局部化与完备化、模型范畴、Hopf代数等。
作者介绍
目录
Introduction
Some conventions and notations
Acknowledgments
PART 1  Preliminaries: Basic Homotopy Theory and Nilpotent Spaces
  1.Cofibrations and fibrations
    1.1  Relations between cofibrations and fibrations
    1.2  The fill-in and Verdier lemmas
    1.3  Based and free cofbrations and fibrations
    1.4  Actions of fundamental groups on homotopy classes of maps
    1.5  Actions of fundamental groups in fibration sequences
  2.Homotopy colimits and homotopy limits; lim1
    2.1  Some basic homotopy colimits
    2.2  Some basic homotopy limits
    2.3  Algebraic properties of lim1
    2.4  Anexample of nonvanishing liml terms
    2.5  The homology of colimits and limits
    2.6  Aprofinite universal coefficient theorem
  3.Nilpotent spaces and Postnikov towers
    3.1  A-nilpotent groups and spaces
    3.2  Nilpotent spaces and Postnikov towers
    3.3  Cocellular spaces and the dual Whitehead theorem
    3.4  Fibrations with fiber an Eilenberg-Mac Lane space
    3.5  Postnikov A-towers
  4.Detecting nilpotent groups and spaces
    4.1  Nilpotent actions and cohomology
    4.2  Universal covers of nilpotent spaces
    4.3  A-maps of A-nilpotent groups and spaces
    4.4  Nilpotency and fibrations
    4.5  Nilpotent spaces and finite type conditions
PART 2  Localizations of Spaces at Sets of Primes
  5.Localizations of nilpotent groups and spaces
    5.1  Localizations of abelian groups
    5.2  The definition of localizations of spaces
    5.3  Localizations of nilpotent spaces
    5.4  Localizations of nilpotent groups
    5.5  Algebraic properties of localizations of nilpotent groups
    5.6  Finitely generated T-local groups
  6.Characterizations and properties of localizations
    6.1  Characterizations of localizations of nilpotent spaces
    6.2  Localizations of limits and fiber sequences
    6.3  Localizations of function spaces
    6.4  Localizations of colimits and cofiber sequences
    6.5  Acellular construction of localizations
    6.6  Localizations of H-spaces and co-H-spaces
    6.7  Rationalization and the finiteness of homotopy groups
    6.8  The vanishing of rational phantom maps
  7.Fracture theorems for localization: groups
    7.1  Global to local pullback diagrams
    7.2  Global to local: abelian and nilpotent groups
    7.3  Local to global pullback diagrams

    7.4  Local to global: abelian and nilpotent groups
    7.5  The genus of abelian and nilpotent groups
    7.6  Exact sequences of groups and pulbacks
  8.Fracture theorems for localization: spaces
    8.1  Statements of the main fracture theorems
    8.2  Fracture theorems for maps into nilpotent spaces
    8.3  Global to local fracture theorems: spaces
    8.4  Local to global fracture theorems: spaces
    8.5  The genus of nilpotent spaces
    8.6  Alternative proofs of the fracture theorems
  9.Rational H-spaces and fracture theorems
    9.1  The structure of rational H-spaces
    9.2  The Samelson product and H* (X; Q)
    9.3  The Whitehead product
    9.4  Fracture theorems for H-spaces
PART 3  Completions of Spaces at Sets of Primes
  10.Completions of nilpotent groups and spaces
    10.1  Completions of abelian groups
    10.2  The definition of completions of spaces at T
    10.3  Completions of nilpotent spaces
    10.4  Completions of nilpotent groups
  11.Characterizations and properties of completions
    11.1  Characterizations of completions of nilpotent spaces
    11.2  Completions of limits and fiber sequences
    11.3  Completions of function spaces
    11.4  Completions of colimits and cofiber sequences
    11.5  Completions of H-spaces
    11.6  The vanishing of p-adic phantom maps
  12.Fracture theorems for completion: groups
    12.1  Preliminaries on pullbacks and isomorphisms
    12.2  Global to local: abelian and nilpotent groups
    12.3  Local to global: abelian and nilpotent groups
    12.4  Formal completions and the adelic genus
  13.Fracture theorems for completion: spaces
    13.1  Statements of the main fracture theorems
    13.2  Global to local fracture theorems: spaces
    13.3  Local to global fracture theorems: spaces
    13.4  The tensor product of a space and a ring
    13.5  Sullivan's formal completion
    13.6  Formal completions and the adelic genus
PART 4  An Introduction to Model Category Theory
  14.An introduction to model category theory
    14.1  Preliminary definitions and weak factorization systems
    14.2  The definition and first properties of model categories
    14.3  The notion of homotopy in a model category
    14.4  The homotopy category of a model category
  15.Cofbrantly generated and proper model categories
    15.1  The small object argument for the construction of WFSs
    15.2  Compactly and cofbrantly generated model categories
    15.3  Over and under model structures

    15.4  Left and right proper model categories
    15.5  Left propernes, lifting properties, and the sets [X, Y]
  16.Categorical perspectives on model categories
    16.1  Derived functors and derived natural transformations
    16.2  Quillen adjunctions and Quillen equivalences
    16.3  Symmetric monoidal categories and enriched categories
    16.4  Symmetricmonoidal and entiched model catesoies
    16.5  A glimpse at higher categoricalstructures
  17.Model structures on the category of spaces
    17.1  The Hurewicz or h-model structure on spaces
    17.2  The Quillen or gmodel structure on spaces
    17.3  Mixed model structures in general
    17.4  The mixed model structure on spaces
    17.5  The model structure on simplicial sets
    17.6  The proof of the model axioms
  18.Model structures on categories of chain complexes
    18.1  The algebraic framework and the analogy with topology
    18.2  h-cofibrations and h-fbrations in ChR
    18.3  The h-model structure on ChR
    18.4  The -model structure on ChR
    18.5  Profs and the characterization of qcofibrations
    18.6  The m-model structure on ChR
  19.Resolution and localization model structures
    19.1  Resolution and mixed model structures
    19.2  The general context of Bousfield localization
    19.3  Localizations with respect to homology theories
    19.4  Bousfield localization at sets and classes of maps
    19.5  Bousfield localization in enriched model categories
PART 5  Bialgebras and Hopf Algebras
  20.Bialgebras and Hopf algebras
    20.1  Preliminaries
    20.2  Algebras, coalgebras, and bialgebras
    20.3  Antipodes and Hopf algebras
    20.4  Modules, comodules, and related concepts
  21.Connected and component Hopf algebras
    21.1  Connected algebras,coalgebras,and Hopf algebras
    21.2  Splitting theorems
    21.3  Component coalgebras and the existence of antipodes
    21.4  Self-dual Hopf algebras
    21.5  The homotopy groups of MO and other Thom spectra
    21.6  A proof of the Bott periodicity theorem
  22.Lie algebras and Hopf algebras in characteristic zero
    22.1  Graded Lie algebras
    22.2  The Poincare-Birkhoff-Witt theorem
    22.3  Primitively generated Hopf algebras in characteristic zero
    22.4  Commutative Hopf algebras in characteristic zero
  23.Restricted Lie algebras and Hopf algebras in characteristic p
    23.1  Restricted Lie algebras
    23.2  The restricted Poincare-Birkhoff-Witt theorem
    23.3  Primitively generated Hopf algebras in characteristic p

    23.4  Commutative Hopf algebras in characteristic p
  24.A primer on spectral sequences
    24.1  Definitions
    24.2  Exact couples
    24.3  Filtered complexes
    24.4  Products
    24.5  The Serre spectral sequence
    24.6  Comparison theorems
    24.7  Convergence proofs
Bibliography
Index

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目