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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

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


Authors: Kimiyo N. Yamamoto and Masahiko Taniguchi
Journal: Conform. Geom. Dyn. 17 (2013), 145-154
MSC (2010): Primary 30F40, 30F45, 30F60
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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Additional Information

Kimiyo N. Yamamoto
Affiliation: Department of Information and Computer Sciences, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
Email: kimiyo520@gmail.com

Masahiko Taniguchi
Affiliation: Department of Mathematics, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
Email: tanig@cc.nara-wu.ac.jp

DOI: http://dx.doi.org/10.1090/S1088-4173-2013-00259-2
PII: S 1088-4173(2013)00259-2
Keywords: Kleinian group, Schottky spaces, cross ratio
Received by editor(s): December 27, 2012
Published electronically: December 30, 2013
Additional Notes: The first author was supported by JSPS Research Fellowship for Young Scientests (PD) (No. 6811).
The second author was partially supported by Grant-in-Aid for Scientific Research (C) (Grant No. 23540202) and (B) (Grant No. 25287021).
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.