Combinatorial Algebraic Topology

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Springer Science & Business Media, Jan 8, 2008 - Mathematics - 390 pages
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Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field.

 

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Contents

I
1
II
5
III
7
V
10
VI
12
VIII
13
IX
15
X
16
CXXXI
192
CXXXII
201
CXXXIV
203
CXXXV
205
CXXXVI
208
CXXXVII
211
CXXXVIII
214
CXXXIX
215

XI
19
XII
23
XIII
25
XIV
28
XVI
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XVII
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XIX
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XX
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XXI
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XXIII
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XXIV
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XXVI
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XXVIII
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XXIX
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XXX
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XXXII
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XXXIII
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XXXV
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XXXVI
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XXXVII
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XXXIX
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XL
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XLI
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XLII
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XLV
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XLVI
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XLVIII
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XLIX
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LI
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LIII
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LIV
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LV
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LVI
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LVIII
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LIX
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LXI
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LXII
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LXIII
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LXIV
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LXV
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LXVI
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LXVII
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LXVIII
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LXIX
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LXX
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LXXI
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LXXII
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LXXIII
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LXXIV
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LXXV
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LXXVI
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LXXVII
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LXXVIII
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LXXIX
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LXXX
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LXXXI
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LXXXII
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LXXXIII
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LXXXIV
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LXXXV
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LXXXVII
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LXXXVIII
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LXXXIX
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XC
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XCI
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XCII
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XCIV
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XCVI
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XCVII
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C
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CI
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CII
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CIV
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CV
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CVI
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CVII
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CVIII
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CIX
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CXII
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CXIII
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CXIV
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CXV
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CXVI
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CXVII
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CXVIII
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CXIX
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CXX
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CXXI
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CXXII
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CXXIII
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CXXIV
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CXXV
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CXXVI
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CXXVII
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CXXVIII
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CXXIX
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CXXX
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CXL
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CXLI
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CXLII
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CXLIII
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CXLIV
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CXLV
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CXLVI
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CXLVII
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CXLVIII
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CXLIX
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CL
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CLI
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CLII
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CLIII
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CLIV
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CLV
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CLVI
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CLVII
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CLVIII
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CLX
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CLXI
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CLXII
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CLXIII
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CLXIV
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CLXV
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CLXVI
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CLXVII
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CLXVIII
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CLXIX
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CLXX
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CLXXI
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CLXXII
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CLXXIII
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CLXXIV
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CLXXV
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CLXXVI
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CLXXVII
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CLXXVIII
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CLXXX
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CLXXXI
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CLXXXII
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CLXXXIII
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CLXXXIV
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CLXXXV
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CLXXXVI
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CLXXXVII
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CLXXXVIII
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CLXXXIX
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CXC
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CXCI
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CXCII
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CXCIII
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CXCIV
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CXCV
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CXCVII
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CXCVIII
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CXCIX
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CC
313
CCI
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CCIII
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CCV
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CCVII
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CCVIII
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CCIX
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CCX
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CCXI
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CCXII
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CCXIII
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CCXIV
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CCXV
334
CCXVI
337
CCXVII
338
CCXIX
340
CCXX
341
CCXXI
346
CCXXII
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CCXXIII
351
CCXXIV
352
CCXXV
353
CCXXVI
354
CCXXVII
355
CCXXIX
356
CCXXX
357
CCXXXI
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CCXXXII
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CCXXXIII
362
CCXXXIV
364
CCXXXV
366
CCXXXVI
367
CCXXXVII
368
CCXXXVIII
370
CCXXXIX
371
CCXL
374
CCXLI
376
CCXLII
377
CCXLIII
385
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About the author (2008)

The author is recipient of Wallenberg Prize of the Swedish Mathematics Society (2003), Gustafsson Prize of the Goran Gustafsson Foundation (2004), and the European Prize in Combinatorics (2005) (see http://www.math.tu-berlin.de/EuroComb05/prize.html for further information). He works at the interface of Discrete Mathematics, Algebraic
Topology, and Theoretical Computer Science.

He has obtained his doctorate from the Royal Institute of Technology, Stockholm in 1996. After longer stays at the Mathematical Sciences Research Institute at Berkeley, the Massachusetts Institute of Technology, the Institute for Advanced Study at Princeton, the University of Washington, Seattle, and Bern University, he has been a Senior Lecturer at the Royal Institute of Technology, Stockholm, and an Assistant Professor at ETH Zurich. Currently he holds the Chair of Algebra and Geometry at the University of Bremen, Germany.

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