L2-Betti numbers of fiber bundles
Bin Sun, Ph.D.; University of Oxford
We study the L²-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 L²-Betti numbers of B. We relate the twisted and untwisted L²-Betti numbers of B when π1(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 Professor Dawid Kielak.
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