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 result from [7], we prove that the moduli space of the stable flat $SL(2,\mathbb{C})$ connections is disconnected under certain technical assumptions.
Teng HUANG
. A COMPACTNESS THEOREM FOR STABLE FLAT $SL(2,\mathbb{C})$ CONNECTIONS ON 3-FOLDS[J]. Acta mathematica scientia, Series B, 2022
, 42(3)
: 1160
-1172
.
DOI: 10.1007/s10473-022-0320-8
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