The symplectic structure of the SL_n(R)-Hitchin component

Geometry & Topology
Event time: 
Tuesday, February 7, 2023 - 4:15pm
LOM 206
Francis Bonahon
Speaker affiliation: 
Event description: 

The SL_n(R)-Hitchin component of a closed surface is a special component in the character variety consisting of homomorphisms from the fundamental group of the surface to the Lie group SL_n(R). It carries a symplectic structure, defined by the Atiyah-Bott-Goldman form. I will provide an explicit computation of this symplectic form in terms of the generalized Fock-Goncharov coordinates of the Hitchin component (associated to a geodesic lamination on the surface).