## Geometry and Topology

•  Ian Montague , Brandeis University
•  Seiberg-Witten Floer K-Theory and Cyclic Group Actions
•  02/21/2023
•  2:00 PM - 3:00 PM
•  C304 Wells Hall
•  Peter Kilgore Johnson (john8251@msu.edu)

Given a spin rational homology sphere equipped with a cyclic group action, I will introduce equivariant refinements of Manolescu's kappa invariant, derived from the equivariant K-theory of the Seiberg--Witten Floer spectrum. These invariants give rise to equivariant relative 10/8-ths type inequalities for equivariant spin cobordisms between rational homology spheres. I will explain how these inequalities provide applications to knot concordance, obstruct cyclic group actions on spin fillings, and give genus bounds for knots in punctured 4-manifolds. If time permits I will explain how these invariants are related to equivariant eta-invariants of the Dirac operator, and describe work-in-progress which provides explicit formulas for the $S^1$-equivariant eta-invariants on Seifert-fibered spaces.

## Contact

Department of Mathematics
Michigan State University