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Combinatorial Algebraic Topology (Algorithms and Computation in Mathematics)
 
 


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Combinatorial Algebraic Topology (Algorithms and Computation in Mathematics) [Paperback]

Dimitry Kozlov
3.7 out of 5 stars  See all reviews (3 customer reviews)

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Book Description

January 8, 2008 3540730516 978-3540730514 2008

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.


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Combinatorial Algebraic Topology (Algorithms and Computation in Mathematics) + Simplicial Complexes of Graphs (Lecture Notes in Mathematics)
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Editorial Reviews

Review

From the reviews:

"This is an introduction to the beautiful world of combinatorial algebraic topology, describing the modern research tools and latest applications in this field. … This could be used as material for a reading seminar on Chromatic numbers and the Kneser Conjecture, structural theory of morphism complexes, characteristic classes and chromatic numbers, applications of spectral sequence to Hom Complexes. … an interesting book with large perspective in studying problems on the borderline between discrete mathematics and algebraic topology." (Corina Mohorianu, Zentralblatt MATH, Vol. 1130 (8), 2008)

“This monograph offers an introduction to combinatorial algebraic topology, an active field connecting algebraic topology with discrete mathematics and computer science. It is intended to be ‘A book to teach from’, providing a self-contained introduction that swiftly guides the reader to the forefront of modern research.” (St. Haller, Monatshefte für Mathematik, Vol. 162 (3), March, 2011)

About the Author

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.


Product Details

  • Series: Algorithms and Computation in Mathematics (Book 21)
  • Paperback: 390 pages
  • Publisher: Springer; 2008 edition (January 8, 2008)
  • Language: English
  • ISBN-10: 3540730516
  • ISBN-13: 978-3540730514
  • Product Dimensions: 6.1 x 0.9 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #731,842 in Books (See Top 100 in Books)

Customer Reviews

3.7 out of 5 stars
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3.7 out of 5 stars
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Top Customer Reviews
1 of 1 people found the following review helpful
5.0 out of 5 stars Very good text May 5, 2013
By Hazard
Format:Paperback|Verified Purchase
This is an excellent text for those wishing to understand Algebraic Topology from a combinatorial or computational viewpoint. The writing is very clear, and, usefully, a lot of the more combinatorial topics are covered that i've not found in any other single source. It was slightly disappointing to not see the connection with geometric topology (like the hauptvermutung and the Zeeman Conjecture) exposited at all, as they are after all still being investigated in some details (with important results announced in the past few months)
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0 of 4 people found the following review helpful
5.0 out of 5 stars |||||||||| Such an Excellent Text |||||||| March 15, 2012
Format:Paperback|Verified Purchase
I happen to know many of the individual topics here. I have not read the book yet, but, I went through the table of contents and browsed the excerpt. Author has taken much pain, we must realize, to put together in a relatively smaller book, large amount of material. AND, in the process has had to teach some basic topics in Alg. Top and Category Theory etc.

Since any author on this subject as in all highly developed fields will be using theorems that are already out there, any other book "in substance" will not differ greatly from this book.

You can of course look up other proofs available elsewhere for theorems hard to appreciate on a particular presentation of it at a particular point in this book.

There should be more excerpt, I think that is one reason others have not commented on it.
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1 of 6 people found the following review helpful
1.0 out of 5 stars Help, where are the editors? March 2, 2009
Format:Paperback
The book is poorly edited.
From the first chapter on, it is very difficult to decipher what the author is trying to say, because of linguistic and typographic errors There are evidently very interesting and useful things in this book, if you are interested in topology, homology and want to know about recent work on simplicial and other complexes, and especially if you are interested in applications to graph theory; but you have to be prepared to work very hard to find out what it is. With a basic introduction to simplicial homology at your side, the first few chapters should make sense.
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