# Poisson maps between character varieties: gluing and capping

@inproceedings{Biswas2021PoissonMB, title={Poisson maps between character varieties: gluing and capping}, author={Indranil Biswas and Jacques Hurtubise and Lisa C. Jeffrey and Sean Lawton}, year={2021} }

. 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…

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