Poisson maps between character varieties: gluing and capping
Algebraic Geometry
2023-04-27 v2 Representation Theory
Symplectic Geometry
Abstract
Let G be a compact Lie group or a complex reductive affine algebraic group. We explore induced mappings between G-character varieties of surface groups by mappings between corresponding surfaces. It is shown that these mappings are generally Poisson. We also given an effective algorithm to compute the Poisson bi-vectors when G=SL(2,C). We demonstrate this algorithm by explicitly calculating the Poisson bi-vector for the 5-holed sphere, the first example for an Euler characteristic -3 surface.
Cite
@article{arxiv.2104.05589,
title = {Poisson maps between character varieties: gluing and capping},
author = {Indranil Biswas and Jacques Hurtubise and Lisa C. Jeffrey and Sean Lawton},
journal= {arXiv preprint arXiv:2104.05589},
year = {2023}
}
Comments
45 pages, 14 figures; accepted for publication in the Journal of Symplectic Geometry