Quasi-Poisson structures on representation spaces of surfaces

2012/05/31 by Gwenael Massuyeau, Vladimir Turaev · 1 citation
Mathematics · #math.GT #math.QA #msc:16W25 #msc:17B63 #msc:53D17 #msc:57M05

paper · pdf

published as Int. Math. Res. Not. 2014:1 (2014) 1-64 · 43 pages. Minor modifications

arxiv created 2012/08/31 · arxiv updated 2014/01/03

Abstract

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 π₁(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 π₁(S,*).

Cited by

• Flat Bundles on Function Manifolds and Evolution Equations in Quantum Field Theories

Related

• On double brackets for marked surfaces
• Double Poisson algebras
• On the variation of the Poisson structures of certain moduli spaces
• Poisson algebras of curves on bordered surfaces and skein quantization
• Poisson Brackets in Kontsevich's "Lie World"