A note on the Mittag–Leffler condition for Bredon-modules

In this note we show the Bredon-analogue of a result by Emmanouil and Talelli, which gives a criterion when the homological and cohomological dimensions of a countable group $G$ agree. We also present some applications to groups of Bredon-homological dimension $1$.Comment: 10 page

On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups

We show that elementary amenable groups, which have a bound on the orders of their finite subgroups, admit a finite dimensional model for the classifying space with virtually cyclic isotropy

On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups

ABSTRACT. We show that every elementary amenable group that has a bound on the orders of its finite subgroups admits a finite dimensional model for EG, the classifying space for actions with virtually cyclic isotropy

The braided Thompson's groups are of type F-infinity

Bux K-U, Fluch MG, Marschler M, Witzel S, Zaremsky M. The braided Thompson's groups are of type F-infinity. Journal für die Reine und Angewandte Mathematik. 2016;718(718):59-101.We prove that the braided Thompson's groups V-br and F-br are of type F-infinity, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an appendix, Zaremsky uses these connectivity results to exhibit families of subgroups of the pure braid group that are highly generating, in the sense of Abels and Holz