Year: 2017
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Huang, Teng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3206031004