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Algebraic topology--homotopy and homology

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The earlier chapters are quite good; however, some of the advanced topics in this book are better approached (appreciated) after one has learned about them elsewhere, at a more leisurely pace. For instance, this isn't the best place to first read about characteristic classes and topological K theory (I would recommend, without much hesitation, the books by Atiyah and Milnor & Stasheff, instead). Much to my disappointment, the chapter on spectral sequences is quite convoluted. Parts of 'user's guide' by Mcleary would certainly come in handy here (which sets the stage rather nicely for applications).

So it turns out that supplemental reading (exluding Whitehead's massive treatise) is necessary to achieve a better understanding of algebraic topology at the level of this book. The homotopical view therein will be matched (possibly superseded) by Aguilar's book (forthcoming, to which I am very much looking forward).

Good luck!

Author(s): Robert M Switzer
Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berucksichtigung der Anwendungsgebiete 212
Publisher: Springer-Verlag
Year: 1975

Language: English
Pages: 543
City: Berlin; New York

Table of Contents......Page 14
0 Some Facts from General Topology......Page 16
1 Categories, Functors and Natural Transformations......Page 21
2 Homotopy Sets and Groups......Page 26
3 Properties of the Homotopy Groups......Page 51
4 Fibrations......Page 67
5 CW-Complexes......Page 79
6 Homotopy Properties of CW-Complexes......Page 89
7 Homology and Cohomology Theories......Page 114
8 Spectra......Page 148
9 Representation Theorems......Page 167
10 Ordinary Homology Theory......Page 182
11 Vector Bundles and K-Theory......Page 205
12 Manifolds and Bordism......Page 233
13 Products......Page 248
14 Orientation and Duality......Page 321
15 Spectral Sequences......Page 351
16 Characteristic Classes......Page 390
17 Cohomology Operations and Homology Cooperations......Page 426
18 The Steenrod Algebra and its Dual......Page 455
19 The Adams Spectral Sequence and the e-Invariant......Page 473
20 Calculation of the Cobordism Groups......Page 505
Bibliography......Page 533
Subject Index......Page 537