Dr. Zhang Ying, National University of Singapore 

Friday, July 15, 4-5pm,

Title:  "Generalized Markoff maps and McShane's identity"

Abstract :
"We study the space of representations of the free group on two generators into SL(2, C) via generalized Markoff maps, following Brian H. Bowditch.

We show that Bowditch's Q-conditions for generalized Markoff maps are  sufficient for the generalized McShane's identity to hold for the corresponding representations.

We also generalize Bowditch's results on variations of McShane's identity for complete, finite volume hyperbolic 3-manifolds which fiber over the circle, with the fiber a punctured-torus,  to identities for (certain) incomplete hyperbolic structures on such
manifolds. 

This is joint work with Ser Peow TAN and Yan Loi WONG of the National University of Singapore.