Topology of matching, chessboard, and general bounded degree graph complexes

Michelle L. Wachs

doi:10.1007/s00012-003-1825-1

Topology of matching, chessboard, and general bounded degree graph complexes

Michelle L. Wachs

Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.

Original language	English (US)
Pages (from-to)	345-385
Number of pages	41
Journal	Algebra Universalis
Volume	49
Issue number	4
DOIs	https://doi.org/10.1007/s00012-003-1825-1
State	Published - 2003

Keywords

Chessboard complex
Matching complex
Simplicial complex

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00012-003-1825-1

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abstract = "We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.",

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note = "Funding Information: Presented by J. Kung. Received September 14, 2001; accepted in final form May 19, 2002. 2000 Mathematics Subject Classification: 05E25, 05E10, 55U10. Key words and phrases: Simplicial complex, matching complex, chessboard complex. The research for this paper was supported in part by NSF grant DMS 0073760.",

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N2 - We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.

AB - We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.

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KW - Matching complex

KW - Simplicial complex

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Topology of matching, chessboard, and general bounded degree graph complexes

Abstract

Keywords

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