Poisson maps between character varieties: gluing and capping

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.

45 pages, 14 figures; accepted for publication in the Journal of Symplectic Geometry

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• The topology of moduli spaces of free group representations
• Poisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary
• Quiver algebras, weighted projective lines, and the Deligne-Simpson problem
• SL(3,C)-Character Varieties and RP2-Structures on a Trinion
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Cited by in corpus (2)

• Flawed groups and the topology of character varieties
• Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus