PSL(2;C) connections on 3-manifolds with L2 bounds on curvature

Abstract

Karen Uhlenbeck's compactness theorem for sequences of connections with L2 bounds on curvature applies only to connections on principal bundles with compact structure group. This article states and proves an extension of Uhlenbecks theorem that describes sequences of connections on principal PSL(2;C) bundles over compact three dimensional manifolds.

This version is a substantial revision of the published version of the article in the Cambridge Journal of Mathematics. This revision fixes some ultimately inconsequential errors and one serious error found by Thomas Walpuski. (Only very minor changes from v3.)

References in corpus (3)

• Fukaya-Seidel category and gauge theory
• Khovanov Homology And Gauge Theory
• Some boundedness properties of solutions to the Vafa-Witten equations on closed four-manifolds

Cited by in corpus (13)

• Asymptotics of certain families of Higgs bundles in the Hitchin component
• Some boundedness properties of solutions to the Vafa-Witten equations on closed four-manifolds
• A sheaf-theoretic model for SL(2,C) Floer homology
• A lower bound on the solutions of Kapustin-Witten equations
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• Seiberg-Witten monopoles with multiple spinors on a surface times a circle
• Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations
• An Energy Gap for Complex Yang-Mills Equations
• The Kapustin-Witten equations and nonabelian Hodge theory
• Index theorem for Z/2-harmonic spinors
• The behavior of sequences of solutions to the Hitchin-Simpson equations
• On a topology property for the moduli space of Kapustin-Witten equations
• A compactness theorem for stable flat $SL(2,\mathbb{C})$ connections on $3$-folds