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arxiv: 1205.4898 · v3 · pith:GFZUDM44new · submitted 2012-05-22 · 🧮 math.GT · math.QA

Quasi-Poisson structures on representation spaces of surfaces

Gwenael Massuyeau , Vladimir Turaev This is my paper
classification 🧮 math.GT math.QA
keywords bracketquasi-poissonalgebraspacebaseberghboundarycanonical
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Given an oriented surface S with base point * on the boundary, we introduce for all N>0, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of \pi_1(S,*). Our bracket extends the well-known Poisson bracket on GL_N-invariant functions on this space. Our main tool is a natural structure of a quasi-Poisson double algebra (in the sense of M. Van den Bergh) on the group algebra of \pi_1(S,*).

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  1. Coupled double Poisson brackets

    math.QA 2026-05 unverdicted novelty 7.0

    Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.