Bredon cohomological finiteness conditions for generalisations of Thompson groups

Speaker: Brita Nucinkis

Speaker organization: Royal Holloway, London

Abstract:

We define a family of groups that generalises Thompson’s groups T and G, 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 Q, there are finitely many conjugacy classes of finite subgroups isomorphic to Q. We use this to show that our groups have a slightly weaker property, quasi-F∞, to that of a group possessing a finite type model for the classifying space for proper actions EG if and only if they posses finite type models for the ordinary classifying space (joint work with C. Martínez-Pérez and Francesco Matucci).