OSU Mathematics Seminars and Colloquia
Wed, Dec 02, 2020
Topology Seminar
3:45 PM
Virtual meeting
Guts, Volume, and Skein Modules of 3-Manifolds
Brandon Bavier, Michigan State University
Host: Neil Hoffman
Contact Neil Hoffman or Henry Segerman for the meeting link.
[Abstract] [PDF]
Abstract: When looking at hyperbolic alternating knots in $S^3$, there is a relation between the twist number, the Jones polynomial, and the volume of the knot complement. Little is known for general hyperbolic links, or links in other manifolds. We consider hyperbolic links that admit alternating projections on surfaces in compact, irreducible 3-manifolds. Under some mild hypotheses, we are able to show that volume of the link complement is bounded below in terms of a Kauffman bracket function defined on link diagrams on the surface. Further, if the manifold is a thickened surface, we can construct a Jones-type polynomial that is an isotopy invariant that leads to a 2-sided linear bound on the volume of hyperbolic alternating links in the thickened surface.
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