Cross ratio coordinates for the deformation spaces of a marked Möbius group

Yamamoto, Kimiyo; Taniguchi, Masahiko

doi:10.1090/S1088-4173-2013-00259-2

Cross ratio coordinates for the deformation spaces of a marked Möbius group
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by Kimiyo N. Yamamoto and Masahiko Taniguchi

Conform. Geom. Dyn. 17 (2013), 145-154

DOI: https://doi.org/10.1090/S1088-4173-2013-00259-2

Published electronically: December 30, 2013

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Abstract:

We introduce a new kind of coordinate systems for the deformation space of a finitely generated free Möbius group by using cross ratio functions induced by the fixed points of Möbius transformations. As an application, we give a new complete distance on the Schottky space by using such functions, which is not greater than the Teichmüller distance.

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