Virtual fibering of manifolds and groups

Sam Fisher (University of Oxford)

Monday 11th March 16:00-17:00 Maths 311B


The question of whether a manifold virtually fibers over the circle is an old and interesting one, and especially so when the manifold is negatively curved in some sense. By the work of Agol and Wise, and it is now known that all hyperbolic 3-manifolds virtually fiber. Recently, a cusped hyperbolic 5-manifold was shown to fiber by Italiano--Martelli--Migliorini, but in general very little is known about which negatively curved high-dimensional manifolds fiber. In this talk, we will explore the group theoretic side of this question. A group algebraically fibers if it admits a homomorphism to Z with finitely generated kernel. We will show that many groups with notions of negative curvature algebraically fiber with kernels having strong finiteness properties and discuss some applications to rank 1 hyperbolic lattices.

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