#### Volume 21, issue 7 (2021)

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

### Nobuo Iida

Algebraic & Geometric Topology 21 (2021) 3303–3333
##### Abstract

Kronheimer and Mrowka (Invent. Math. 130 (1997) 209–255) constructed a variant of Seiberg–Witten invariants for a $4$–manifold $X$ with contact boundary. Using Furuta’s finite-dimensional approximation, we refine this invariant in the case ${H}^{1}\left(X,\partial X;ℝ\right)=0$.

##### Keywords
3–manifold, 4–manifold, contact structure, symplectic structure, gauge theory, Seiberg–Witten equation, Bauer–Furuta invariant, Kronheimer–Mrowka invariant for 4–manifolds with contact boundary
##### Mathematical Subject Classification 2010
Primary: 57R17, 57R57
##### Publication
Received: 27 July 2019
Revised: 12 August 2020
Accepted: 4 January 2021
Published: 28 December 2021
##### Authors
 Nobuo Iida Graduate School of Mathematical Sciences The University of Tokyo Tokyo Japan