Some remarks on finite 1-acyclic and collapsible complexes

Yoav Segev

doi:10.1016/0097-3165(94)90041-8

Some remarks on finite 1-acyclic and collapsible complexes

Yoav Segev

Department of Mathematics

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

5 Scopus citations

Abstract

Let G be a finite group. Assume that G acts (simplicially) on a finite simplicial complex D. We show that if dim(D) = 2 and D is collapsible, G fixes a point of |D|. We also show that if G has no composition factor of Lie-type and Lie-rank 1, or the Sporadic J₁, dim(D) = 3 and D is collapsible, G fixes a point of |D|. In addition we obtain various results on collapsible complexes and a certain tree decomposition of a finite connected simplicial complex D, such that H₁(D) = 0.

Original language	English
Pages (from-to)	137-150
Number of pages	14
Journal	Journal of Combinatorial Theory - Series A
Volume	65
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(94)90041-8
State	Published - 1 Jan 1994

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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abstract = "Let G be a finite group. Assume that G acts (simplicially) on a finite simplicial complex D. We show that if dim(D) = 2 and D is collapsible, G fixes a point of |D|. We also show that if G has no composition factor of Lie-type and Lie-rank 1, or the Sporadic J1, dim(D) = 3 and D is collapsible, G fixes a point of |D|. In addition we obtain various results on collapsible complexes and a certain tree decomposition of a finite connected simplicial complex D, such that H1(D) = 0.",

author = "Yoav Segev",

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N2 - Let G be a finite group. Assume that G acts (simplicially) on a finite simplicial complex D. We show that if dim(D) = 2 and D is collapsible, G fixes a point of |D|. We also show that if G has no composition factor of Lie-type and Lie-rank 1, or the Sporadic J1, dim(D) = 3 and D is collapsible, G fixes a point of |D|. In addition we obtain various results on collapsible complexes and a certain tree decomposition of a finite connected simplicial complex D, such that H1(D) = 0.

AB - Let G be a finite group. Assume that G acts (simplicially) on a finite simplicial complex D. We show that if dim(D) = 2 and D is collapsible, G fixes a point of |D|. We also show that if G has no composition factor of Lie-type and Lie-rank 1, or the Sporadic J1, dim(D) = 3 and D is collapsible, G fixes a point of |D|. In addition we obtain various results on collapsible complexes and a certain tree decomposition of a finite connected simplicial complex D, such that H1(D) = 0.

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Some remarks on finite 1-acyclic and collapsible complexes

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