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

TL;DR

This paper extends a known homological dimension criterion to Bredon-modules, providing new insights into the dimensions of groups and applications for groups with Bredon-homological dimension one.

Contribution

It introduces a Bredon-analogue of a key homological dimension result and explores its implications for specific classes of groups.

Findings

Established a Bredon-analogue of the Emmanouil and Talelli criterion.

Provided applications to groups with Bredon-homological dimension 1.

Enhanced understanding of homological dimensions in the context of Bredon-modules.

Abstract

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 $1$.