On the asymptotic behavior of complex earthquakes and Teichm\"{u}ller disks
Geometric Topology
2013-11-21 v1 Differential Geometry
Abstract
Given a hyperbolic surface and a simple closed geodesic on it, complex-twists along the curve produce a holomorphic family of deformations in Teichm\"{u}ller space, degenerating to the Riemann surface where it is pinched. We show there is a corresponding Teichm\"{u}ller disk such that the two are strongly asymptotic, in the Teichm\"{u}ller metric, around the noded Riemann surface. We establish a similar comparison with plumbing deformations that open the node.
Keywords
Cite
@article{arxiv.1311.4933,
title = {On the asymptotic behavior of complex earthquakes and Teichm\"{u}ller disks},
author = {Subhojoy Gupta},
journal= {arXiv preprint arXiv:1311.4933},
year = {2013}
}
Comments
19 pages, to appear in a Contemp. Math. proceedings