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$L^2$-homology and Sigma invariants

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Sam Hughes
University of Oxford
Wed, 15/05/2024 - 11:30 - 12:30
MPIM Lecture Hall
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 $\mathbb Z$; $L^2$ 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 $L^2$ 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.
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