Affordable Access

Yang-Mills connections on surfaces and representations of the path group

Authors
  • Morrison, Kent E.
Type
Published Article
Publication Date
Nov 24, 2014
Submission Date
Nov 24, 2014
Identifiers
arXiv ID: 1411.6676
Source
arXiv
License
Yellow
External links

Abstract

We prove that Yang-Mills connections on a surface are characterized as those with the property that the holonomy around homotopic closed paths only depends on the oriented area between the paths. Using this we have an alternative proof for a theorem of Atiyah and Bott that the Yang-Mills connections on a compact orientable surface can be characterized by homomorphisms to the structure group from an extension of the fundamental group of the surface. In addition, we obtain the results that the Yang-Mills connections on the sphere are isolated and correspond with the conjugacy classes of closed geodesics through the identity in the structure group.

Report this publication

Statistics

Seen <100 times