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

Iida, Nobuo

doi:10.2140/agt.2021.21.3303

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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

DOI: 10.2140/agt.2021.21.3303

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 $H^{1} (X, \partial X; ℝ) = 0$ .

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

Volume 21, issue 7 (2021)