A compactness theorem for stable flat SL(2,ℂ) connections on 3-folds

2017/06/12 by Teng Huang, Huang, Teng
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1706.03486

openalex publication_date 2017/06/12 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

Let Y be a closed 3-manifold such that all flat SU(2)-connections on Y are non-degenerate. In this article, we prove a Uhlenbeck-type compactness theorem on Y for stable flat SL(2,ℂ) connections satisfying an L²-bound for the real curvature. Combining the compactness theorem and a previous result in \citeHuang, we prove that the moduli space of the stable flat SL(2,ℂ) connections is disconnected under certain technical assumptions.

Citations

• The Self-Duality Equations on a Riemann Surface
• PSL(2;C) connections on 3-manifolds with L2 bounds on curvature

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