3-Manifold Seminar: Profinite rigidity for groups and 3-manifolds
Seminar | October 3 | 2:10-3:30 p.m. | 740 Evans Hall
Nic Brody, UC Berkeley
The profinite completion of the fundamental group $G$ of a 3-manifold $M$ is an assemblage of the possible finite quotients of $G$. If a $G$ has profinite completion different from that of any distinct $\pi _1 N$, $N$ a 3-manifold, then we say that $G$ is profinitely rigid. We will see some positive and negative results in the study of profinite rigidity, and review some open questions in this area. Highlights include Hempel's construction of non-homeomorphic surface bundles with all the same finite covers, and Bridson-Reid-Wilton's proof that punctured torus bundles over the circle are profinitely rigid among 3-manifold groups.