Realizing the Teichm\"uller space as a symplectic quotient
Differential Geometry
2019-09-26 v1 Symplectic Geometry
Abstract
Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the natural action of the group of volume-preserving diffeomorphisms by push-forward has a group-valued momentum map that assigns to a Riemannian metric the canonical bundle. We then deduce that the Teichm\"uller space and the moduli space of Riemann surfaces can be realized as symplectic orbit reduced spaces.
Keywords
Cite
@article{arxiv.1909.11551,
title = {Realizing the Teichm\"uller space as a symplectic quotient},
author = {Tobias Diez and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:1909.11551},
year = {2019}
}
Comments
To be published in RIMS K\^oky\^uroku