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Combinatorial Algebraic Topology
Buch von Dimitry Kozlov
Sprache: Englisch

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Beschreibung
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. 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.
Über den Autor

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 [...] 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.

Zusammenfassung

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. Readers 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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Topologie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 412
Reihe: Algorithms and Computation in Mathematics
Inhalt: xx
390 S.
115 s/w Illustr.
390 p. 115 illus.
ISBN-13: 9783540719618
ISBN-10: 354071961X
Sprache: Englisch
Herstellernummer: 11936756
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kozlov, Dimitry
Auflage: 2008
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Algorithms and Computation in Mathematics
Maße: 241 x 160 x 27 mm
Von/Mit: Dimitry Kozlov
Erscheinungsdatum: 24.10.2007
Gewicht: 0,781 kg
preigu-id: 102026834
Über den Autor

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 [...] 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.

Zusammenfassung

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. Readers 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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Topologie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 412
Reihe: Algorithms and Computation in Mathematics
Inhalt: xx
390 S.
115 s/w Illustr.
390 p. 115 illus.
ISBN-13: 9783540719618
ISBN-10: 354071961X
Sprache: Englisch
Herstellernummer: 11936756
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kozlov, Dimitry
Auflage: 2008
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Algorithms and Computation in Mathematics
Maße: 241 x 160 x 27 mm
Von/Mit: Dimitry Kozlov
Erscheinungsdatum: 24.10.2007
Gewicht: 0,781 kg
preigu-id: 102026834
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