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edited title

edited Mar 4, 2016 at 4:44

Is a non-flat hermitian connection determined uniquely by its holonomy and curvature?

How do I prove that gauge-equivalence classes of $U(1)$ connections on a line bundle $L\to M$ are determined uniquely by pairs $(\alpha,F)$, where $$\alpha\in\text{Hom}(\pi_1(M),U(1)),~~~~F\in \Omega^2(M)?$$

dg.differential-geometry connections

asked Mar 3, 2016 at 12:58

David Roberts