Geometry/topology Seminar
Monday, September 10, 2018, 3:15pm, 119 Physics
Richard Hain (Duke University, Mathematics)
Hodge theory and the Goldman-Turaev Lie bialgebra
Abstract:- In the 1980s, Bill Goldman used intersection theory to define
a Lie algebra structure on the free Z module L(X) generated by the
closed geodesics on a hyperbolic surface X. This bracket is related to
a formula for the Poisson bracket of functions on the variety of flat
G-bundles over X. In related work (1970s and 1990s), Vladimir Turaev
(with contributions by Kawazumi and Kuno in the 2000s) constructed a
cobracket on L(X) that depends on the choice of a framing. In this
talk, I will review the definition of the Goldman-Turaev Lie bialgebra
of a framed surface and discuss its relevance to questions in other
areas of mathematics. I'll discuss how Hodge theory can be applied to
these questions. I may also discuss some related questions, such as
the classification of mapping class group orbits of framings of a
punctured surface. [video]
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