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Group actions on finite acyclic simplicial complexes

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Abstract

In this paper we develop some homological techniques to obtain fixed points for groups acting on finite Z-acyclic complexes. In particular we show that if a groupG acts on a finite 2-dimensional acyclic simplicial complexD, then the fixed point set ofG onD is either empty or acyclic. We supply some machinery for determining which of the two cases occurs. The Feit-Thompson Odd Order Theorem is used in obtaining this result.

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Yoav Segev

Authors
  1. Yoav Segev
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Additional information

This paper is dedicated to Prof. John G. Thompson on the occasion of receiving the Wolf Prize, 1992

This work was partially supported by BSF 88-00164.

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Segev, Y. Group actions on finite acyclic simplicial complexes. Israel J. Math. 82, 381–394 (1993). https://doi.org/10.1007/BF02808120

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  • DOI: https://doi.org/10.1007/BF02808120

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