Discreteness for energies of Yang-Mills connections over four-dimensional manifolds
Paul Feehan (Rutgers University)
Tuesday 16th June, 2015 16:00-17:00 Maths 204
We show that for any principal bundle with compact Lie structure group over a closed, four-dimensional, Riemannian manifold, the L^2 energies of Yang-Mills connections on a principal bundle form a discrete sequence without accumulation points. Our proof employs a version of our Lojasiewicz-Simon gradient inequality for the Yang-Mills L^2-energy functional extensions of our previous results on the bubble-tree compactification for the moduli space of anti-self-dual connections to the moduli space of Yang-Mills connections with a uniform L2 bound on their energies. We expect that a similar argument should hold for the energies of harmonic maps of closed Riemann surfaces into real-analytic, closed, Riemannian manifolds, thus verifying a 1999 conjecture of Fanghua Lin.