《單純同倫理論(英文)》指出自從開啟了代數拓撲現代領域的新紀元，單純方法已經在計算方面和基本理論方面很系統化並且有效化。隨著Quillen的封閉模型類，特別是單純模型類概念的發展，這個方法已經成為描述非阿貝爾同倫代數的最基本方法，也是表述眾多領域，包括K理論的同倫理論觀點的重要途徑。
基本介紹
- 書名：單純同倫理論
- 作者：格茲 (Paul G.Goerss)
- 出版日期：2014年3月1日
- 語種：簡體中文, 英語
- ISBN：9787510070327
- 外文名：Simplicial Homotopy Theory
- 出版社：世界圖書出版公司北京公司
- 頁數：510頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《單純同倫理論(英文)》為這些觀點的一個重要補充表述，強調了模型類理論技巧。
作者簡介
作者：（美國）格茲（Paul G.Goerss） （美國）John F.Jardine
圖書目錄
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
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
