## Seminar September 20 – Will Cavendish

On September 20, the geometry-topology seminar hosts Will Cavendish of Princeton University. He will speak about:

Title: Finite sheeted covers of 3-manifolds and the cohomology of solenoids

Abstract: Given a compact manifold $M$, the inverse limit of the set of all
finite sheeted covering spaces over $M$ yields a compact topological
space $\widehat{M}$ called a solenoid that can be thought of as a
pro-finite version of the universal cover of $M$. While such an
object can in general be quite complicated, I will show in this talk
that if $M$ is a compact aspherical 3-manifold then $\widehat{M}$ has the
Cech cohomology of a disk. I will then talk about the relevance of
this result to the study of finite sheeted covering spaces and lifting
problems in 3-manifold theory.

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