Alex Suciu

Abstract: The Bieri-Neumann-Strebel-Renz invariants Σⁱ(G, Z) of a finitely generated group G hold subtle information about the homological finiteness properties of normal subgroups N < G with abelian quotients. The actual computation of the Σ-invariants is enormously complicated, and has been achieved so far only for some special classes of groups.

In this talk, I will present some computable upper bounds for the Σ-invariants, in terms of the exponential tangent cones to the jump loci for homology with coefficients in rank 1 local systems. Under suitable hypothesis, these bounds can be expressed in terms of simpler data, namely, the resonance varieties associated to the cohomology ring of G. These techniques yield information on groups arising in a variety of geometric and topological contexts, such as right-angled Artin groups and Artin kernels, 3-manifold groups, as well as Kähler and quasi-Kähler groups.

This is joint work with Stefan Papadima.

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.