The quasi-Poisson Goldman formula

TL;DR

This paper extends Goldman's Poisson bracket formula to a quasi-Poisson setting for surface groupoid representations, providing new formulas for quasi-Poisson cross-sections.

Contribution

It generalizes Goldman's Poisson bracket to a quasi-Poisson context and derives a corresponding formula for quasi-Poisson cross-sections.

Findings

Proved a quasi-Poisson bracket formula for surface groupoid representations.

Generalized Goldman's Poisson bracket to quasi-Poisson structures.

Derived a formula for quasi-Poisson cross-sections.

Abstract

We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.