JournalsggdVol. 7, No. 4pp. 931–959

Bredon cohomological finiteness conditions for generalisations of Thompson groups

  • Conchita Martínez-Pérez

    Universidad de Zaragoza, Spain
  • Brita E. A. Nucinkis

    Royal Holloway University of London, Egham, UK
Bredon cohomological finiteness conditions for generalisations of Thompson groups cover
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Abstract

We define a family of groups that generalises Thompson’s groups TT and GG, and also those of Higman, Stein and Brin. For groups in this family we describe centralisers of finite subgroups and show that for a given finite subgroup QQ there are finitely many conjugacy classes of finite subgroups isomorphic to QQ. We consider groups of type quasi-F\underline{\rm F}_\infty. This is a property slightly weaker than possessing a finite type model for the classifying space for proper actions EG\underline{E}G. We give criteria for the TT versions of our groups to be of type quasi-F\underline{\rm F}_\infty. We also generalise some well-known properties of ordinary cohomology to Bredon cohomology.

Cite this article

Conchita Martínez-Pérez, Brita E. A. Nucinkis, Bredon cohomological finiteness conditions for generalisations of Thompson groups. Groups Geom. Dyn. 7 (2013), no. 4, pp. 931–959

DOI 10.4171/GGD/211