Combinatorial Algebraic Topology

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Springer Science & Business Media, Oct 24, 2007 - 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
2
II
6
III
7
IV
36
V
59
VI
77
VII
88
VIII
101
XIV
210
XV
225
XVI
245
XVII
258
XVIII
275
XIX
290
XX
293
XXI
309

IX
111
X
126
XI
127
XII
151
XIII
179
XXII
327
XXIII
348
XXIV
377
XXV
385
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About the author (2007)

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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