University of Arkansas Topology Seminar: 2/4/2021

Speaker: Robert Kropholler

Title: Algebraic fibering for surface bundles

The simplest form of surface bundle is a fibered 3–manifold. Generalising from this we are interested in the class of surface bundles with surface group base. We are interested in what properties these bundles have in common with fibered 3–manifolds, in particular we are interested in the properties of coherence and fibering for their fundamental groups. I will motivate the class of groups we will study and discuss surrounding results. I will then talk about recent work with S. Vidussi and G. Walsh showing that such a bundle is coherent if and only if one of the surfaces is a torus, this answers a question of Hillman. I will also connect fibering to the virtual first Betti number of the mapping class group.



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