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Geometry-Topology Seminar

Thursday, March 25, 2021 - 4:30pm

Katherine Raoux

Michigan State University


University of Pennsylvania

via Zoom

The Zoom link is: This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (, Davi Maximo ( or Herman Gluck (

A null-homologous knot in a 3-manifold bounds a surface in the 3-manifold and, if you can compute the knot Floer homology, you can compute the minimal genus of such a surface. However, if we realize the 3-manifold as the boundary of some 4-manifold, the knot may bound a surface of smaller genus in the 4-manifold. While we can’t always compute this minimal genus precisely, we can use tools from Heegaard Floer theory, particularly the tau-invariant, to produce lower bounds. I will discuss the tau-invariant, a recent generalization due to Hedden and myself, and corresponding genus bounds. I will also discuss some applications to links and contact manifolds. 

This is joint work with Matthew Hedden.