单纯同伦理论 epub pdf mobi txt 电子书 下载 2024

单纯同伦理论 epub pdf mobi txt 电子书 下载 2024

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单纯同伦理论 epub pdf mobi txt 电子书 下载 2024

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内容简介

　　Many of the original research and survey monographs ln pure and applied mathematics published by Birkh iuser in recent decades have been groundbreaking and have come to be regarded as found。 ational to the SUbject．Through the MBC Series，a select number ofthese modern classics，entirely uncorrected，are being released in paperback Iand as eBooks)to ensure that these treasures remainaccessible to new generations of students，scholars，and reseat-chers。

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目录

Chapter l Simplicial sets

1．Basic definitions

2．Realization

3．Kan complexes

4．Anodyne extensions

5．Function complexes

6．Simplicial homotopy

7．Simplicial homotopy groups

8．Fundamental groupoid

9．Categories of fibrant objects

10．Minimal fibrations

11．The closed model structure

Chapter II Model Categories

1．Homotopical algebra

2．Simplicial categories

3．Simplicial model categories

4．The existence of simplicial model category structures

5．Examples of simplicial model categories

6．A generalization of Theorem 4．1

7．Quillen’S total derived functor theorem

8．Homotopy cartesian diagrams

Chapter III Classical results and constructions

1．The fundamental groupoid．revisited

2．Simplicial abelian groups

3．The Hurewicz map

4．The Ex∞functor

5．The Kan suspension

Chapter IV Bisimplicial sets

1．Bisimplicial sets：first properties

2．Bisimplicial abelian groups

2．1．The translation object

2．2 The generalized Eilenberg-Zilber theorem

3．Closed model structures for bisimplicial sets

3．1．The Bousfield-Kan structure

3．2．The Reedy structure

3．3．The Moerdijk structure

4．The Bousfield―Friedlander theorem

5．Theorem B and group completion

5．1．The’serre spectral sequence

5．2．Theorem B

5．3．The group completion theorem

Chapter V Simplicial groups

1．Skeleta

2．Principal fibrations I：simplicial G-spaces

3．Principal fibrations II：classifications

4．Universal cocycles and WG

5．The loop group construction

6．Reduced simplicial sets，Milnor’S FK-construction

7．Simplicial groupoids

Chapter VI The homotopy theory of towers

1．A model category structure for towers of spaces

2．The spectral sequence of a tower of fibrations

3．Postnikov towers

4．Local coefficients and equivariant cohomology

5．On k-invariants

6．Nilpotent spaces

Chapter VII Reedy model categories

1．Decomposition of simplicial objects

2．Reedy model category structures

3．Geometric realization

4．Cosimplicial spaces

Chapter VIII Cosimplicial spaces：applications

1．The homotopy spectral sequence of a cosimplicial space

2．Homotopy inverse limits

3．Completions

4．Obstruction theory

Chapter IX Simplicial functors and homotopy coherence

1．Simplicial functors

2．The Dwyer-Kan theorem

3．Homotopy coherence

3．1．Classical homotopy COherence

3．2．Homotopy coherence：an expanded version

3．3．Lax functors

3．4．The Grothendieck construction

4．Realization theorems

Chapter X Localization

1．Localization with respect to a map

2．The closed model category structure

3．Bousfield localization．

4．A model for the stable homotopy category

References

Index

前言/序言

单纯同伦理论 epub pdf mobi txt 电子书 下载 2024

单纯同伦理论 下载 epub mobi pdf txt 电子书 2024

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原本是去年看完Munkres《代数拓扑基础》中译本之后写成的文章，一年之后自然又有了一些新收获，所以就补充一点新的体会重发出来。 先来说说读这个书所需要的预备知识，主要就是代数与拓扑两个方面的了。其实书中对一些基础的知识都预先做了大致的介绍，所以起点还是比较低的，但若是已经掌握一些基本技术，那么就可以把注意集中到拓扑的主要内容上了。代数方面，最好了解一点模正合列，特别是要把图表追赶的技术玩熟.这本书写的很好，有些较难的概念也都能解释的很透彻，比国内出版的大多数拓扑学基础的书好很多。还有一本也是Munkres写的《拓扑学基本教程》，这本书特别适合刚刚接触拓扑的人看。只是现在国内不再印了。很可惜...

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本书根据James R．Munkres所著“Elements of Algebraic Topology” (Perseus出版社1993年版)译出。.

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