Simplicial complexes of graphs

A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial comp...

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Main Author: Jonsson, Jakob
Format: Book
Language:English
Published: Springer 2017
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Online Access:http://repository.vnu.edu.vn/handle/VNU_123/29870
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Institution: Vietnam National University, Hanoi
Language: English
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spelling oai:112.137.131.14:VNU_123-298702020-06-19T09:31:03Z Simplicial complexes of graphs Jonsson, Jakob Topological graph theory Morse theory 511.5 A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes. 2017-04-17T07:46:27Z 2017-04-17T07:46:27Z 2008 Book 9783540758587 http://repository.vnu.edu.vn/handle/VNU_123/29870 en 376 p. application/pdf Springer
institution Vietnam National University, Hanoi
building VNU Library & Information Center
country Vietnam
collection VNU Digital Repository
language English
topic Topological graph theory
Morse theory
511.5
spellingShingle Topological graph theory
Morse theory
511.5
Jonsson, Jakob
Simplicial complexes of graphs
description A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
format Book
author Jonsson, Jakob
author_facet Jonsson, Jakob
author_sort Jonsson, Jakob
title Simplicial complexes of graphs
title_short Simplicial complexes of graphs
title_full Simplicial complexes of graphs
title_fullStr Simplicial complexes of graphs
title_full_unstemmed Simplicial complexes of graphs
title_sort simplicial complexes of graphs
publisher Springer
publishDate 2017
url http://repository.vnu.edu.vn/handle/VNU_123/29870
_version_ 1680967446569156608