Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

K. Guruprasad

Vol. 162 (1994), No. 1, 45–55

DOI: 10.2140/pjm.1994.162.45

Abstract

In this paper we associate a new geometric invariant to the space of flat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it to the symplectic structure on the space Hom(π₁(M),G)∕G consisting of representations of the fundamental group π₁(M) of M into G modulo the conjugate action of G on representations.

Mathematical Subject Classification 2000

Primary: 58D27

Secondary: 57R57, 58F05

Milestones

Received: 23 December 1991

Published: 1 January 1994