Journal of Symplectic Geometry

Volume 20 (2022)

Number 1

Monopoles and foliations without holonomy-invariant transverse measure

Pages: 191 – 258

DOI: https://dx.doi.org/10.4310/JSG.2022.v20.n1.a5

Author

Boyu Zhang (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.; and Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Abstract

This article proves a uniform exponential decay estimate for Seiberg–Witten equations on non-compact $4$‑manifolds with exact symplectic ends of bounded geometry. This is an extension of the analysis for asymptotically flat almost Kähler (AFAK) structures by Kronheimer and Mrowka [17]. As an application, we construct an invariant for smooth foliations without holonomy-invariant transverse measure, which takes value in the boundary-stable version of the monopole Floer homology group introduced by Kronheimer and Mrowka [18], without invoking the Eliashberg–Thurston perturbation.

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Received 6 December 2016

Accepted 29 May 2021

Published 21 October 2022