Mathematics – Geometric Topology
Scientific paper
2007-07-20
Mathematics
Geometric Topology
17 pages, 1 figure
Scientific paper
In this paper we consider the action of the mapping class group of a surface on the space of homomorphisms from the fundamental group of a surface into PSL(2,R). Goldman conjectured that when the surface is closed and of genus bigger than one, the action on non-Teichmuller connected components of the associated moduli space (i.e. the space of homomorphisms modulo conjugation) is ergodic. One approach to this question is to use sewing techniques which requires that one considers the action on the level of homomorphisms, and for surfaces with boundary. In this paper we consider the case of the one-holed torus with boundary condition, and we determine regions where the action is ergodic. Our main result mirrors a theorem of Goldman's at the level of moduli.
No associations
LandOfFree
The action of the mapping class group on representation varieties of PSL(2,R). Case I: The one-holed torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The action of the mapping class group on representation varieties of PSL(2,R). Case I: The one-holed torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The action of the mapping class group on representation varieties of PSL(2,R). Case I: The one-holed torus will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-399244