Chennai Mathematical Institute


3:30 pm, Seminar Hall
Goldman bracket: center and geometric intersection number

Arpan Kabiraj
Chennai Mathematical Institute.


In 1980s Goldman introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F. This Lie bracket is known as the Goldman bracket and the Lie algebra is known as the Goldman Lie algebra.

In this talk I will discuss some basic properties of Goldman bracket and its relation with Teichmüller space. I will als o sho how techniques from geometric group theory could be used to compute center of the Goldman Lie algebra. I will mention some open problems related to Goldman bracket. If time permits, I will show a method to compute geometric intersection number using Goldman bracket.