We explore a weakening of the coherence property of discrete groups studied by F.
Waldhausen. The new notion is defined in terms of the coarse geometry of groups and …

We prove that one-relator groups are coherent, solving a well-known problem of Gilbert
Baumslag. Our proof strategy is readily applicable to many classes of groups of …

Bounded-cohomological dimension of groups is a relative of classical cohomological
dimension, defined in terms of bounded cohomology with trivial coefficients instead of …

Let G be a group that admits a cocompact classifying space for proper actions X. We derive
a formula for the Bredon cohomological dimension for proper actions of G in terms of the …

Using Auslander's G-dimension, we assign a numerical invariant to any group Γ. It provides
a refinement of the cohomological dimension and fits well into the well-known hierarchy of …

Group cohomology of polynomial growth is defined for any finitely generated discrete group,
using cochains that have polynomial growth with respect to the word length function. We …

We introduce panels of stabilizer schemes (K, G∗) associated with finite intersection‐closed
subgroup sets ℋ of a given group G, generalizing in some sense Davis' notion of a panel …

In this expository paper we describe some recent work in the cohomology of finite groups. In
particular, we discuss techniques for calculation and how they apply to key examples from …

1. Introduction. G roup theorists find cohomology of groups a confusing and difficult subject:
a great deal of formalism is necessary to formulate the subject while the applications to …

This paper has three parts. It is conjectured that for every elementary amenable group G and
every non-zero commutative ring k, the homological dimension hd k (G) is equal to the …