On the asymptotic behavior of complex earthquakes and Teichm\"{u}ller disks

Subhojoy Gupta

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arXiv · 1311.4933

On the asymptotic behavior of complex earthquakes and Teichm\"{u}ller disks

Subhojoy Gupta

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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.

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Subhojoy Gupta. 2013-11-20. On the asymptotic behavior of complex earthquakes and Teichm\"{u}ller disks. https://arxiv.org/abs/1311.4933

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