Mirzakhani's work on earthquake flow
Dynamical Systems
2021-09-14 v2 Geometric Topology
Abstract
The Teichmuller unipotent flow can be defined concretely on certain moduli spaces of singular flat surfaces by shearing polygonal presentations of the surfaces. Thurston's earthquake flow on moduli spaces of hyperbolic surfaces is more mysterious. Both flows have deep and important connections to other areas of mathematics. In this expository survey we give a geometric account of the main ideas behind Mirzakhani's theorem relating these two flows. Our presentation avoids some technical prerequisites that featured in the original more analytic presentation.
Keywords
Cite
@article{arxiv.1810.07571,
title = {Mirzakhani's work on earthquake flow},
author = {Alex Wright},
journal= {arXiv preprint arXiv:1810.07571},
year = {2021}
}
Comments
v2: Expanded introduction; rewrote final part of Section 2; minor edits throughout