The limit set of non-orientable mapping class groups
Sayantan Khan (Michigan)
Abstract: The study of moduli spaces and mapping class groups of compact orientable hyperbolic surfaces has been guided by strong analogies with finite volume hyperbolic surfaces and their fundamental groups. For the moduli spaces and mapping class group of compact non-orientable surfaces, there is evidence to believe that an analogy can be made with infinite volume geometrically finite hyperbolic surfaces.
In this talk, we present some results that provide evidence for this analogy, the main one being a partial description of the limit set in the Thurston boundary, and a result that shows that the analogy is imperfect: we show that a conjectured convex core is not even quasi-convex.