William Gryc

Lecturer at Georgia State University

On the Holonomy of the Coulomb Connection over 3-Manifolds with Boundary

Leonard Gross

Functional analysis and mathematical physics

Abstract: Narasimhan and Ramadas showed in [NR] that the Gribov ambiguity was maximal in the case where the principal bundle is the trivial SU(2) bundle over S³. This maximality comes in the form of the holonomy group of the Coulomb connection being dense in the gauge group. Here we consider a different situation where the base manifold has a boundary (unlike S³). In this with-boundary case we must consider boundary conditions, and consider so-called conductor boundary conditions on connections. With these boundary conditions, we show that the connections over the gauge orbits is indeed a C^∞ Hilbert principal bundle on which we can consider the holonomy of the Coulomb connection. In the case of the base manifold being an open subset of R³ and a trivial principal bundle, we show that the holonomy group is again a dense subset of the gauge group, showing that the Gribov ambiguity is also maximal in this case.

PhD

PhD