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Topology/Geometry Seminar

\(\ell^2\)-homology and Sigma invariants

Sam Hughes (University of Oxford)

Location:  Online
Date & time: Tuesday, 20 February 2024 at 4:00PM - 5:00PM

Based on joint work with Dawid Kielak. In this talk I will give an overview of two families of invariants of a group: the Sigma invariants encode geometrically information about fibrings of \(G\) over the integers \(\mathbb{Z}\); \(\ell^2\) homology on the other hand is an equivariant homology that accounts for all unitary representations of the group. A classical result of Wolfgang Lück shows that non-vanishing of \(\ell^2\) homology obstructs the existence of mapping tori structures, here we will generalise this result to the BNSR invariants and discuss some of the difficulties that arise.