Quasi-Poisson structures on representation spaces of surfaces (Q2878681)
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scientific article; zbMATH DE number 6340326
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasi-Poisson structures on representation spaces of surfaces |
scientific article; zbMATH DE number 6340326 |
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5 September 2014
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quasi-Poisson structures
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invariant functions
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group algebra
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representations
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Poisson bracket
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Fox pairings
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Fuchsian groups
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Quasi-Poisson structures on representation spaces of surfaces (English)
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This paper generalizes the well-known Poisson bracket to invariant functions on representation spaces of surfaces. First, the authors give the definition of quasi-Poisson algebras. The theory of Van den Bergh is recalled and it is shown how to derive double brackets from Fox pairings. The canonical quasi-Poisson bracket is introduced. Finally, the authors consider moment maps and discuss surfaces without boundary. The extension of the construction to Fuchsian groups is also described.
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