Equivariant discrete Morse theory

Ragnar Freij

doi:10.1016/j.disc.2008.10.029

Equivariant discrete Morse theory

Ragnar Freij^*

^*Corresponding author for this work

Not published at Aalto University

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

20 Citations (Scopus)

Abstract

In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, we determine the C₂ × S_{n - 2}-homotopy type of the complex of non-connected graphs on n nodes.

Original language	English
Pages (from-to)	3821-3829
Number of pages	9
Journal	Discrete Mathematics
Volume	309
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2008.10.029
Publication status	Published - 28 Jun 2009
MoE publication type	A1 Journal article-refereed

Keywords

Discrete Morse theory
Equivariant homotopy
Graph complexes

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10.1016/j.disc.2008.10.029

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title = "Equivariant discrete Morse theory",

abstract = "In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, we determine the C2 × Sn - 2-homotopy type of the complex of non-connected graphs on n nodes.",

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N2 - In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, we determine the C2 × Sn - 2-homotopy type of the complex of non-connected graphs on n nodes.

AB - In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, we determine the C2 × Sn - 2-homotopy type of the complex of non-connected graphs on n nodes.

KW - Discrete Morse theory

KW - Equivariant homotopy

KW - Graph complexes

UR - http://www.scopus.com/inward/record.url?scp=67349168758&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2008.10.029

DO - 10.1016/j.disc.2008.10.029

M3 - Article

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SN - 0012-365X

VL - 309

SP - 3821

EP - 3829

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 12

ER -

Equivariant discrete Morse theory

Abstract

Keywords

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