Simplicial Homotopy Theory (Google eBook)

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Springer Science & Business Media, Jan 1, 1999 - Mathematics - 510 pages
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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.

  

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Contents

I
1
II
3
III
7
IV
9
V
14
VI
20
VII
23
VIII
25
XLII
251
XLIII
252
XLIV
260
XLV
265
XLVI
269
XLVII
275
XLVIII
285
XLIX
295

IX
36
X
40
XI
47
XII
59
XIII
65
XIV
66
XV
81
XVI
89
XVII
97
XVIII
101
XIX
109
XX
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XXI
121
XXII
139
XXIII
140
XXIV
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XXV
165
XXVI
182
XXVII
189
XXVIII
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XXIX
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XXX
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XXXI
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XXXII
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XXXIII
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XXXIV
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XXXVI
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XXXVII
223
XXXVIII
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XXXIX
234
XL
237
XLI
242
L
307
LI
309
LII
315
LIII
326
LIV
329
LV
342
LVI
350
LVII
353
LIX
364
LX
373
LXI
376
LXII
389
LXIII
390
LXIV
400
LXV
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LXVI
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LXVII
431
LXIX
437
LXX
449
LXXII
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LXXIII
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LXXIV
455
LXXV
457
LXXVI
463
LXXVII
464
LXXVIII
478
LXXIX
489
LXXX
492
LXXXI
503
LXXXII
507
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Model Categories
Mark Hovey
No preview available - 1999
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