ENGLISH

Simplicial Complexes of Graphs

By Jakob Jonsson (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2008
ISBN
3540758585, 978-3-540-75858-7
DOI
10.1007/978-3-540-75859-4
Open Library ID
OL16156326M
Language
english
Format
PDF
Filesize
3 MB (3319429 bytes)
Series
Lecture Notes in Mathematics 1928
Edition
1
Pages
382\367
Library
mexmat
Time added
2009-07-20 03:45:11
Combinatorics; Algebraic Topology; OrderLatticesOrdered Algebraic Structures

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.

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