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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 H1(X,X; ) = 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
References
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