Bounding the homological finiteness length

We give a criterion for bounding the homological finiteness length of certain HF-groups. This is used in two distinct contexts. Firstly, the homological finiteness length of a non-uniform lattice on a locally finite n-dimensional contractible CW-complex is less than n. In dimension two it solves a conjecture of Farb, Hruska and Thomas. As another corollary, we obtain an upper bound for the homological finiteness length of arithmetic groups over function fields. This gives an easier proof of a result of Bux and Wortman that solved a long-standing conjecture. Secondly, the criterion is applied to integer polynomial points of simple groups over number fields, obtaining bounds established in earlier works of Bux, Mohammadi and Wortman, as well as new bounds. Moreover, this verifes a conjecture of Mohammadi and Wortman.Comment: Revised versio

Orbits of strongly solvable spherical subgroups on the flag variety

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable combinatorial invariants. As well, we study the Weyl group action defined by Knop on the set of H-orbits in G/B, and we give a combinatorial model for this action in terms of weight polytopes.Comment: v4: final version, to appear on Journal of Algebraic Combinatorics. Apported some minor corrections to the previous versio

Homological stability for automorphism groups of RAAGs

We show that the homology of the automorphism group of a right-angled Artin group stabilizes under taking products with any right-angled Artin group.Comment: final versio

The Farrell-Jones conjecture for fundamental groups of graphs of abelian groups

We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups