Fock-Goncharov coordinates for rank 2 Lie groups

Geometry Topology Seminar
Monday, June 6, 2016 - 14:05
1 hour (actually 50 minutes)
Skiles 114
University of Maryland
We discuss the higher Teichmuller space A_{G,S} defined by Fockand Goncharov. This space is defined for a punctured surface S withnegative Euler characteristic, and a semisimple, simply connected Lie groupG. There is a birational atlas on A_{G,S} with a chart for each idealtriangulation of S. Fock and Goncharov showed that the transition functionsare positive, i.e. subtraction-free rational functions. We will show thatwhen G has rank 2, the transition functions are given by explicit quivermutations.