Department of Mathematics

Geometry and Topology

  •  Bin Sun, Oxford
  •  $L^2$-Betti numbers of fiber bundles
  •  09/20/2022
  •  3:00 PM - 4:00 PM
  •  C304 Wells Hall (Virtual Meeting Link)
  •  Vijay B Higgins (

We study the $L^2$-Betti numbers of fiber bundles $F \rightarrow E \rightarrow B$ 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 $\pi_1(B)$ 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.



Department of Mathematics
Michigan State University
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