Monopoles and foliations without holonomy-invariant transverse measure

2016/03/26 by Boyu Zhang, Zhang, Boyu
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Geometry and complex manifolds #math.GT #msc:53D05 #msc:57R30 #msc:57R58

paper · pdf · doi:10.48550/arxiv.1603.08136

47 pages

arxiv created 2021/06/02 · arxiv updated 2021/06/03

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. 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, without invoking the Eliashberg-Thurston perturbation.

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