Title: On type-preserving representations of thrice punctured projective plane group
Speaker: Sara Maloni (University of Virginia)
Abstract: In this talk we consider type-preserving representations of the fundamental group of the three-holed projective plane $N$ into $PGL(2, \mathbb{R})$. First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch. In addition, we show also, in most cases, that the action of the pure mapping class group Mod($N$) on these non-maximal components is ergodic.
This is joint work with F. Palesi and T. Yang.
