### L^{2}-Betti numbers of fiber bundles

Geometry and Topology Seminar

8th November 2022, 2:00 pm – 3:00 pm

Fry Building, 2.04

We study the L^{2}-Betti numbers of fiber bundles F → E → B of manifolds. Under certain conditions (e.g., when F is simply connected), b_{*}^{(2)}(E) can be computed using the twisted L^{2}-Betti numbers of B. We relate the twisted and untwisted L^{2}-Betti numbers of B when π_{1}(B) is locally indicable. As an application, we compute b_{*}^{(2)}(E) when B is either a surface or a non-positively curved 3-manifold. This is a joint work with Dawid Kielak.

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