Topological dynamics on moduli spaces, I

Joseph P. Previte and Eugene Z. Xia

Vol. 193 (2000), No. 2, 397–417

DOI: 10.2140/pjm.2000.193.397

Abstract

Let M be a one-holed torus with boundary ∂M (a circle) and Γ the mapping class group of M fixing ∂M. The group Γ acts on ℳ_𝒞(SU(2)) which is the space of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on ∂M. We study the topological dynamics of the Γ-action and give conditions for the individual Γ-orbits to be dense in ℳ_𝒞(SU(2)).

Milestones

Received: 2 September 1998

Revised: 28 January 1999

Published: 1 April 2000