Symplectic double for moduli spaces of G-local systems on surfaces
Algebraic Geometry
2015-05-21 v2 Geometric Topology
Quantum Algebra
Abstract
Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, considered modulo isotopy. We introduce a moduli space D(G,S) and define a collection of special rational coordinate systems on it. The moduli space D(G,S) is the symplectic double of the Poisson moduli space of framed G-local systems on S. Its symplectic form is upgraded to a K2-symplectic structure for which the special coordinates are K2-Darboux coordinates.
Keywords
Cite
@article{arxiv.1410.3526,
title = {Symplectic double for moduli spaces of G-local systems on surfaces},
author = {Vladimir Fock and Alexander Goncharov},
journal= {arXiv preprint arXiv:1410.3526},
year = {2015}
}
Comments
Dedicated to the memory of Andrei Zelevinsky. Version 2: Introduction expanded. To appear in Advances Math