Tian Yang will be visiting from Stanford to give the topology seminar next Thursday (Feb 26), and will be around all day Thursday. Let me know if you'd like to go to lunch with us that day, or meet with Tian etc.
Here are Tian's talk title and abstract:
*On type-preserving representations of the four-punctured sphere group*
*Abstract:* We give counterexamples to a conjecture of Bowditch that if a non-elementary type-preserving representation ρ : π1(Σg,n) → PSL(2; R) of a punctured surface group sends every non-peripheral simple closed curve to a hyperbolic element, then ρ must be Fuchsian. The counterexamples come from relative Euler class +/-1 representations of the four-punctured sphere group. As a related result, we show that the mapping class group action on each non-extremal component of the character space of type-preserving representations of the four-punctured sphere group is ergodic. The main tool we use is Penner's lengths coordinates of the decorated character spaces defined by Kashaev.
Henry