Simple geodesics and a series constant over Teichmuller space
- Cite this article as:
- McShane, G. Invent math (1998) 132: 607. doi:10.1007/s002220050235
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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.