Date/Time
Date(s) - 05/12/2024
3:30 pm - 4:30 pm

Location: Hamilton Hall, Room 312

Speaker: Tamara Hogan (University of Toronto)

Title: A knot theoretic interpretation of the Goldman-Turaev Lie bialgebra

Abstract: Arising in the early study of string topology, the Goldman-Turaev Lie bialgebra is a well-studied structure on the space of free immersed loops on a surface of genus g with n+1 punctures. The bracket and co-bracket in this structure involve smoothings of intersections between pairs of loops or between a loop and itself. More recently, in a series of papers, Alekseev, Kawazumi, Kuno and Naef showed that expansions (or finite-type invariants) of these structures are equivalent to solutions of the Kashiwara-Vergne (KV) equations. A similar correspondence between expansions of welded tangles and solutions to the KV equations is known due to Bar-Natan and Dancso. Motivated by trying to understand the connection between these two different spaces and their expansions, in this talk I will describe the construction of a lift of the Goldman-Turaev structure in genus zero to the space of tangles in a handlebody. This is joint work with Dror Bar-Natan, Zsuzsanna Dancso, Jessica Liu and Nancy Scherich.