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Seiberg–Witten and Gromov invariants for self-dual harmonic $2$–forms

Chris Gerig

Geometry & Topology 26 (2022) 3307–3365
DOI: 10.2140/gt.2022.26.3307
Abstract

Our earlier work (Geom. Topol. 24 (2020) 1791–1839) gives an extension of Taubes’ “ SW = Gr ” theorem to nonsymplectic 4–manifolds. The main result of this sequel asserts the following: whenever the Seiberg–Witten invariants are defined over a closed minimal 4–manifold X, they are equivalent modulo 2 to “near-symplectic” Gromov invariants in the presence of certain self-dual harmonic 2–forms on X. A version for nonminimal 4–manifolds is also proved. A corollary to Morse theory on 3–manifolds is also announced, recovering a result of Hutchings, Lee, and Turaev about the 3–dimensional Seiberg–Witten invariants.

Keywords
near-symplectic, Seiberg–Witten, Gromov, pseudoholomorphic, ECH, monopole Floer
Mathematical Subject Classification 2010
Primary: 53D42, 57R57
References
Publication
Received: 16 October 2018
Revised: 18 April 2021
Accepted: 29 July 2021
Published: 16 March 2023
Proposed: Simon Donaldson
Seconded: Ciprian Manolescu, Leonid Polterovich
Authors
Chris Gerig
Department of Mathematics
UC Berkeley
Berkeley, CA
United States