Simplicial Homotopy Theory

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Springer Science & Business Media, 05.12.2009 - 510 Seiten
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Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques.

Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature.

Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Reviews:

"... a book filling an obvious gap in the literature and the authors have done an excellent job on it. No monograph or expository paper has been published on this topic in the last twenty-eight years." - Analele Universitatii din Timisoara

"... is clearly presented and a brief summary preceding every chapter is useful to the reader. The book should prove enlightening to a broad range of readers including prospective students and researchers who want to apply simplicial techniques for whatever reason." - Zentralblatt MATH

 "... they succeed. The book is an excellent account of simplicial homotopy theory from a modern point of view [...] The book is well written. [...] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques and/or the theory of (simplicial) closed model categories." - Mathematical Reviews

 

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Inhalt

I
1
II
3
III
7
IV
9
V
14
VI
20
VII
23
VIII
25
XXXV
252
XXXVI
260
XXXVII
269
XXXVIII
275
XXXIX
285
XL
295
XLI
307
XLII
309

IX
36
X
40
XI
47
XII
59
XIII
65
XIV
66
XV
81
XVI
89
XVII
97
XVIII
101
XIX
109
XX
115
XXI
121
XXII
139
XXIII
140
XXIV
145
XXV
165
XXVI
182
XXVII
189
XXVIII
195
XXIX
196
XXX
200
XXXI
211
XXXII
223
XXXIII
233
XXXIV
251
XLIII
315
XLIV
326
XLV
329
XLVI
342
XLVII
350
XLVIII
353
L
364
LI
373
LII
376
LIII
389
LIV
390
LV
400
LVI
412
LVII
417
LVIII
431
LX
437
LXI
449
LXII
457
LXIII
463
LXIV
464
LXV
478
LXVI
489
LXVII
492
LXVIII
503
LXIX
507
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