Abstract. We show that Brin's generalisations 2V and 3V of the Thompson-Higman group V are of type FP∞. Our methods also give a new proof that both groups are finitely presented.
We consider the cohomology of Mackey functors for infinite groups and define the Mackeycohomological dimension cd M G of a group G. We will relate this dimension to other cohomological dimensions such as the Bredon-cohomological dimension cd F G and the relative cohomological dimension F-cdG. In particular, we show that for virtually torsion free groups the Mackeycohomological dimension is equal to both F-cdG and the virtual cohomological dimension.
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 consider a slightly weaker property, quasi-F ∞ , to that of a group possessing a finite type model for the classifying space for proper actions EG, and give criteria for the T versions of our groups to be of type quasi-F ∞ . We also generalise some well-known properties of ordinary cohomology to Bredon cohomology.
Abstract. We show that the mapping class group of a closed surface admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.