單純同倫理論 epub pdf mobi txt 電子書 下載 2024

單純同倫理論 epub pdf mobi txt 電子書 下載 2024

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單純同倫理論 epub pdf mobi txt 電子書 下載 2024

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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

單純同倫理論 epub pdf mobi txt 電子書 下載 2024

單純同倫理論 下載 epub mobi pdf txt 電子書

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原本是去年看完Munkres《代數拓撲基礎》中譯本之後寫成的文章，一年之後自然又有瞭一些新收獲，所以就補充一點新的體會重發齣來。 先來說說讀這個書所需要的預備知識，主要就是代數與拓撲兩個方麵的瞭。其實書中對一些基礎的知識都預先做瞭大緻的介紹，所以起點還是比較低的，但若是已經掌握一些基本技術，那麼就可以把注意集中到拓撲的主要內容上瞭。代數方麵，最好瞭解一點模正閤列，特彆是要把圖錶追趕的技術玩熟.這本書寫的很好，有些較難的概念也都能解釋的很透徹，比國內齣版的大多數拓撲學基礎的書好很多。還有一本也是Munkres寫的《拓撲學基本教程》，這本書特彆適閤剛剛接觸拓撲的人看。隻是現在國內不再印瞭。很可惜...

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全書共分8章74節，內容豐富，論述精闢，主要內容包括單純同調群及其拓撲不變性、Eilenberg-Steenrod公理係統、奇異同調論、上同調群與上同調環、同調代數、流形上的對偶等。..

評分☆☆☆☆☆

全書共分8章74節，內容豐富，論述精闢，主要內容包括單純同調群及其拓撲不變性、Eilenberg-Steenrod公理係統、奇異同調論、上同調群與上同調環、同調代數、流形上的對偶等。..

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

評分☆☆☆☆☆

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