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Combinatorial Algebraic Topology by Kozlov, Dimitry

by Kozlov, Dimitry | HC | VeryGood
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Oggetto che si trova a: Aurora, Illinois, Stati Uniti
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“May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend ...
Binding
Hardcover
Book Title
Combinatorial Algebraic Topology
Weight
1 lbs
Product Group
Book
IsTextBook
No
ISBN
9783540719618

Informazioni su questo prodotto

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
354071961X
ISBN-13
9783540719618
eBay Product ID (ePID)
22038751485

Product Key Features

Number of Pages
Xx, 390 Pages
Publication Name
Combinatorial Algebraic Topology
Language
English
Subject
Group Theory, Algebra / Abstract, Topology, Discrete Mathematics
Publication Year
2007
Type
Textbook
Subject Area
Mathematics
Author
Dmitry Kozlov
Series
Algorithms and Computation in Mathematics Ser.
Format
Hardcover

Dimensions

Item Height
0.4 in
Item Weight
27.5 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
Dewey Edition
22
Reviews
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), 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 fr Mathematik, Vol. 162 (3), March, 2011), 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)
Series Volume Number
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
514.22
Table Of Content
Concepts of Algebraic Topology.- Overture.- Cell Complexes.- Homology Groups.- Concepts of Category Theory.- Exact Sequences.- Homotopy.- Cofibrations.- Principal ?-Bundles and Stiefel--Whitney Characteristic Classes.- Methods of Combinatorial Algebraic Topology.- Combinatorial Complexes Melange.- Acyclic Categories.- Discrete Morse Theory.- Lexicographic Shellability.- Evasiveness and Closure Operators.- Colimits and Quotients.- Homotopy Colimits.- Spectral Sequences.- Complexes of Graph Homomorphisms.- Chromatic Numbers and the Kneser Conjecture.- Structural Theory of Morphism Complexes.- Using Characteristic Classes to Design Tests for Chromatic Numbers of Graphs.- Applications of Spectral Sequences to Hom Complexes.
Synopsis
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. 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. 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., 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., 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.
LC Classification Number
QA612-612.8

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