Positive-square obstruction to ASD line connections
= Positive-square obstruction to ASD line connections
{title2=$c_1(L)^2[X]\leq0$}
An <anti-self-dual connection> on a line bundle has $c_1(L)^2[X]=-\|iF_A/(2\pi)\|_2^2\leq0$. A line bundle with positive square therefore admits no such connection for any metric of the chosen orientation. The splitting $L\oplus L^{-1}$ has $c_2=-c_1(L)^2$, giving the equivalent nonnegative-instanton-charge obstruction.
// Destination: geometry-and-topology.bigb