Realizing the Teichmüller space as a symplectic quotient

Wednesday, 25 September, 2019

Published in: 

arXiv:1909.11551

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 Teichmüller space and the moduli space of Riemann surfaces can be realized as symplectic orbit reduced spaces.

Author(s): 

Tobias Diez
Tudor S. Ratiu