Home /  GT Graduate Student Seminar: Seiberg-Witten Floer K-Theory and Cyclic Group Actions on Spin 4-Manifolds with Boundary

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: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Ian Montague (Brandeis University)
Description No Description
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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 register 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's 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.

No Notes/Supplements Uploaded

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