Institute of Mathematics for Industry

Seminar



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Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for 4-manifolds with contact boundary


Hold Date 2020-01-17 16:00~2020-01-17 17:00

Place Seminar Room W1-C-615, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Nobuo IIDA (University of Tokyo)

Abstract:
The Seiberg-Witten invariant is an invariant for closed 4-manifolds and there are many variants of it. I construct a new variant of the Seiberg-Witten invariant based on two previous works. First, Bauer and Furuta refined the Seiberg-Witten invariant, and made an invariant called the stable cohomotopy invariant, which is an S^1- equivariant stable homotopy map obtained by Furuta's finite dimensional approximation of the Seiberg-Witten map. Second, Kronheimer and Mrowka defined a variant of the Seiberg-Witten invariant for 4-manifolds with contact boundary. I combine these two variants of the Seiberg-Witten invariant; that is, using Furuta's finite dimensional approximation, I refine Kronheimer-Mrowka's invariant for 4-manifolds with contact boundary.