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Seminar

GT Graduate Student Seminar: Seiberg-Witten Floer K-Theory and Cyclic Group Actions on Spin 4-Manifolds with Boundary September 20, 2022 (10:00 AM PDT - 11:00 AM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Ian Montague (Brandeis University)
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GT Graduate Student Seminar: Seiberg-Witten Floer K-Theory And Cyclic Group Actions On Spin 4-Manifolds With Boundary

Abstract/Media

To participate in this seminar, please registerĀ HERE.

Given a spin rational homology sphere Y equipped with a Z/m-action preserving the spin structure, I will outline how to define equivariant refinements of Manolescu'sĀ kappa invariant. These invariants give rise to equivariant relative 10/8-ths type inequalities for Z/m equivariant spin cobordisms between rational homology spheres. I will explain how these inequalities provide applications to knot concordance, give obstructions to extending cyclic group actions to spin fillings, and via taking branched covers give us genus bounds for knots in punctured 4-manifolds. In some cases, these bounds are strong enough to determine the genus for a large class of knots within certain homology classes in 4-manifolds with b_+=2.

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GT Graduate Student Seminar: Seiberg-Witten Floer K-Theory And Cyclic Group Actions On Spin 4-Manifolds With Boundary