William Gryc

William Gryc
Ph.D. (2006) Cornell University

First Position

Lecturer at Georgia State University

Dissertation

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

Advisor:


Research Area:
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.