College of Liberal Arts & Sciences
Graduate Geometry Seminar
Speaker:
Charles Frohman
Abstract:
Starting from Bill Goldman’s formula for the Poisson structure on Teichmüller space, we give an explicit formula for the Poisson bracket in terms of un-oriented simple diagrams. This leads to a state sum formula for the Poisson bracket which makes it resemble the state function underlying the product structure on the Kauffman bracket skein algebra of $F$. Next we use this to show that the Kauffman bracket skein algebra of a surface is a quantization of Teichmüller space. We finish with a conjectural picture of the representation variety of the Kauffman bracket skein algebra of a closed oriented surface at a root of unity.
Event Date:
March 8, 2019 - 3:30pm to 4:30pm
Location:
B13
Calendar Category:
Seminar
Seminar Category:
Geometry and Topology