Gauge-Theoretic aspects of parabolic bundles over real curves

Abstract

We study the gauge-theoretic aspects of real and quaternionic parabolic bundles over a real curve ( X , σ X ) , where X is a compact Riemann surface and σ X is an anti-holomorphic involution. For a fixed real or quaternionic structure on a smooth parabolic bundle, we examine the orbits space of real or quaternionic connections under the appropriate gauge group. The corresponding gauge-theoretic quotients sit inside the real points of the moduli of holomorphic parabolic bundles having a fixed parabolic type on a compact Riemann surface X .