Heat flow on the moduli space of flat connections and Yang-Mills theory

2010/08/02 by Janner, Remi
#53C07 #53D20 (Secondary) #58E05 #58E05 (Primary) 53C22 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1008.0257

Abstract

It is known that there is a bijection between the perturbed closed geodesics, below a given energy level, on the moduli space of flat connections M and families of perturbed Yang-Mills connections depending on a small parameter. In this paper we study the heat flow on the loop space on M and the Yang-Mills L²-flows for a 3-manifold N with partial rescaled metrics. Our main result is that the bounded Morse homology of the loop space on M is isomorphic to the bounded Morse homologies of the connections space of N.

Related

• Elliptic Yang-Mills Flow Theory
• The Yang-Mills Gradient Flow and Loop Spaces of Compact Lie Groups
• The Yang-Mills heat flow on the moduli space of framed bundles on a surface
• Morse theory for the Yang-Mills energy function near flat connections
• Continuity of the Yang-Mills flow on the set of semistable bundles