Stable finiteness properties of infinite discrete groups

Structural Properties of Inner Amenable Discrete Groups

Homological and Finiteness Properties of Picture Groups

Picture groups are a class of groups introduced by Guba and Sapir. Known examples include Thompson’s groups F , T , and V . In this paper, a large class of picture groups is proved to be of type F∞. A Morse-theoretic argument shows that, for a given picture group, the rational homology vanishes in almost all dimensions.

Jumping loci and finiteness properties of groups

Characteristic varieties. Let X be a connected CW-complex with finitely many cells in each dimension, and G its fundamental group. The characteristic varieties of X are the jumping loci for cohomology with coefficients in rank 1 local systems: V i k (X) = {ρ ∈ Hom(G,C∗) | dimH(X,Cρ) ≥ k}. These varieties emerged from the work of Novikov [22] on Morse theory for closed 1-forms on manifolds. It t...

Improving Finiteness Properties for Metabelian Groups

We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. The proof builds upon work of G. Baumslag [4], who independently with V. R. Remeslennikov [10] proved that any finitely generated metabelian group can be embedded in a finitely presented one. We also rely essentially on the Sigma theory of R. Bieri and R. Strebel [7], who introduced this geome...

Finiteness of the Stable Homotopy Groups of Spheres