, Volume 132, Issue 3, pp 607-632

Simple geodesics and a series constant over Teichmuller space

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Abstract

We investigate the Birman Series set in a neighborhood of a cusp on a punctured surface, showing that it is homeomorphic to a Cantor set union countably many isolated points cross a line. The local topology of the Cantor set is shown to be related in a simple way to the global behavior of simple geodesics. From this we deduce that a certain series is constant across the Teichmuller space.

Oblatum IV-1995 & 5-VI-1997