## 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 (higgi231@msu.edu)

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.

## Contact

Department of Mathematics
Michigan State University