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☆☆☆☆☆

[英] 格茲 著

齣版社： 世界圖書齣版公司

ISBN：9787510070327

版次：1

商品編碼：11457445

包裝：平裝

叢書名： 經典數學叢書

開本：24開

齣版時間：2014-03-01

用紙：膠版紙

頁數：510

內容簡介

　　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。

內頁插圖

目錄

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

評分☆☆☆☆☆

評分☆☆☆☆☆

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評分☆☆☆☆☆

由於作者獨具匠心的靈活編排，使得本書能適閤於多種教學需要，如可作為研究生一學年或學期的教材，也可供本科高年級選修課選用，此外本書可供廣大科技工作者和拓撲學愛好者閱讀。...

評分☆☆☆☆☆

由於作者獨具匠心的靈活編排，使得本書能適閤於多種教學需要，如可作為研究生一學年或學期的教材，也可供本科高年級選修課選用，此外本書可供廣大科技工作者和拓撲學愛好者閱讀。...

評分☆☆☆☆☆

本書根據James R．Munkres所著“Elements of Algebraic Topology” (Perseus齣版社1993年版)譯齣。.