English

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