单纯同伦理论

图书标准信息

• 作者 [英]格兹 著
• 出版社 世界图书出版公司
• 出版时间 2014-03
• 版次 1
• ISBN 9787510070327
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 510页
• 丛书 经典数学丛书

【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。

【目录】

ChapterlSimplicialsets

1．Basicdefinitions

2．Realization

3．Kancomplexes

4．Anodyneextensions

5．Functioncomplexes

6．Simplicialhomotopy

7．Simplicialhomotopygroups

8．Fundamentalgroupoid

9．Categoriesoffibrantobjects

10．Minimalfibrations

11．Theclosedmodelstructure

ChapterIIModelCategories

1．Homotopicalalgebra

2．Simplicialcategories

3．Simplicialmodelcategories

4．Theexistenceofsimplicialmodelcategorystructures

5．Examplesofsimplicialmodelcategories

6．AgeneralizationofTheorem4．1

7．Quillen’Stotalderivedfunctortheorem

8．Homotopycartesiandiagrams

ChapterIIIClassicalresultsandconstructions

1．Thefundamentalgroupoid．revisited

2．Simplicialabeliangroups

3．TheHurewiczmap

4．TheEx∞functor

5．TheKansuspension

ChapterIVBisimplicialsets

1．Bisimplicialsets：firstproperties

2．Bisimplicialabeliangroups

2．1．Thetranslationobject

2．2ThegeneralizedEilenberg-Zilbertheorem

3．Closedmodelstructuresforbisimplicialsets

3．1．TheBousfield-Kanstructure

3．2．TheReedystructure

3．3．TheMoerdijkstructure

4．TheBousfield―Friedlandertheorem

5．TheoremBandgroupcompletion

5．1．The’serrespectralsequence

5．2．TheoremB

5．3．Thegroupcompletiontheorem

ChapterVSimplicialgroups

1．Skeleta

2．PrincipalfibrationsI：simplicialG-spaces

3．PrincipalfibrationsII：classifications

4．UniversalcocyclesandWG

5．Theloopgroupconstruction

6．Reducedsimplicialsets，Milnor’SFK-construction

7．Simplicialgroupoids

ChapterVIThehomotopytheoryoftowers

1．Amodelcategorystructurefortowersofspaces

2．Thespectralsequenceofatoweroffibrations

3．Postnikovtowers

4．Localcoefficientsandequivariantcohomology

5．Onk-invariants

6．Nilpotentspaces

ChapterVIIReedymodelcategories

1．Decompositionofsimplicialobjects

2．Reedymodelcategorystructures

3．Geometricrealization

4．Cosimplicialspaces

ChapterVIIICosimplicialspaces：applications

1．Thehomotopyspectralsequenceofacosimplicialspace

2．Homotopyinverselimits

3．Completions

4．Obstructiontheory

ChapterIXSimplicialfunctorsandhomotopycoherence

1．Simplicialfunctors

2．TheDwyer-Kantheorem

3．Homotopycoherence

3．1．ClassicalhomotopyCOherence

3．2．Homotopycoherence：anexpandedversion

3．3．Laxfunctors

3．4．TheGrothendieckconstruction

4．Realizationtheorems

ChapterXLocalization

1．Localizationwithrespecttoamap

2．Theclosedmodelcategorystructure

3．Bousfieldlocalization．

4．Amodelforthestablehomotopycategory

References

Index