Inventiones mathematicae

, Volume 132, Issue 3, pp 607–632

Simple geodesics and a series constant over Teichmuller space


  • Greg McShane
    • Laboratoire de Mathématique, Université Paul Sabatier, F-31062 Toulouse, France

DOI: 10.1007/s002220050235

Cite this article as:
McShane, G. Invent math (1998) 132: 607. doi:10.1007/s002220050235


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.

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© Springer-Verlag Berlin Heidelberg 1998