Poisson maps between character varieties: gluing and capping
Indranil Biswas, Jacques Hurtubise, Lisa C. Jeffrey, Sean Lawton

TL;DR
This paper investigates Poisson maps between G-character varieties induced by surface mappings, providing an algorithm for computing Poisson bi-vectors, exemplified on a 5-holed sphere with Euler characteristic -3.
Contribution
It establishes that these induced maps are generally Poisson and introduces an effective algorithm for computing Poisson bi-vectors for G=SL(2,C).
Findings
Mappings are generally Poisson.
Algorithm successfully computes Poisson bi-vectors.
Explicit example for a 5-holed sphere provided.
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
