Conformal Dehn surgery and the shape of Maskit’s embedding

Parkkonen, Jouni

doi:10.1090/S1088-4173-04-00116-X

Conformal Dehn surgery and the shape of Maskit’s embedding
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by Jouni Parkkonen

Conform. Geom. Dyn. 8 (2004), 143-157

DOI: https://doi.org/10.1090/S1088-4173-04-00116-X

Published electronically: October 14, 2004

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Abstract:

We study the geometric limits of sequences of loxodromic cyclic groups which arise from conformal Dehn surgery. The results are applied to obtain an asymptotic description of the shape of the main cusp of the Maskit embedding of the Teichmüller space of once-punctured tori.

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The geometry and topology of three-manifolds

The shape of the boundary of Maskit’s embedding of the Teichmüller space of punctured tori