A compactness theorem for stable flat $SL(2,\mathbb{C})$ connections on $3$-folds

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 $SL(2,\mathbb{C})$ connections satisfying an $L^2$-bound for the real curvature. Combining the compactness theorem and a previous result in \cite{Huang}, we prove that the moduli space of the stable flat $SL(2,\mathbb{C})$ connections is disconnected under certain technical assumptions.

15 pages, Accepted in Acta Mathematica Scientia

References in corpus (2)

• A lower bound on the solutions of Kapustin-Witten equations
• An Energy Gap for Complex Yang-Mills Equations