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arXiv · 1909.11551

Realizing the Teichm\"uller space as a symplectic quotient

Tobias Diez·Tudor S. Ratiu
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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.

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Tobias Diez, Tudor S. Ratiu. 2019-09-25. Realizing the Teichm\"uller space as a symplectic quotient. https://arxiv.org/abs/1909.11551

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