Let M be a four-holed sphere and γ the mapping class group of M fixing ∂M. The group γ acts on the space ℳ ℬ(SU(2)) of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on ∂M. We give examples of flat SU(2)-connections whose holonomy groups are dense in SU(2), but whose γ-orbits are discrete in ℳℬ(SU(2)), This phenomenon does not occur for surfaces with genus greater than zero.
All Science Journal Classification (ASJC) codes
- Applied Mathematics