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

Abstract

Kronheimer and Mrowka constructed a variant of Seiberg-Witten invariants for a 4-manifold $X$ with contact boundary in 1997. Using Furuta's finite dimensional approximation, we refine this invariant in the case $H^1(X, \partial X; \mathbb{R})=0$.