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Conformal Geometry and Dynamics

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Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$

Authors: Thomas Gauglhofer and Klaus-Dieter Semmler
Journal: Conform. Geom. Dyn. 9 (2005), 46-75
MSC (2000): Primary 32G15, 30F35; Secondary 11F06
Published electronically: April 26, 2005
MathSciNet review: 2133805
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Abstract: We explicitly give $\mathcal{T}$, the Teichmüller space of four-holed spheres (which we call X pieces) in trace coordinates, as well as its modular group and a fundamental domain for the action of this group on $\mathcal{T}$ which is its moduli space. As a consequence, we see that on any hyperbolic Riemann surface, two closed geodesics of lengths smaller than $2\operatorname{arccosh}(2)$ intersect at most once; two closed geodesics of lengths smaller than $2\operatorname{arccosh}(3)$ are both non-dividing or intersect at most once.

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Additional Information

Thomas Gauglhofer
Affiliation: EPFL SB IGAT GEOM, Bâtiment MA, Station 8, CH-1015 Lausanne (Switzerland)

Klaus-Dieter Semmler
Affiliation: EPFL SB IGAT GEOM, Bâtiment MA, Station 8, CH-1015 Lausanne (Switzerland)

Received by editor(s): September 3, 2003
Received by editor(s) in revised form: February 8, 2005
Published electronically: April 26, 2005
Additional Notes: The authors were supported in part by the Swiss National Science Foundation, SNSF Grant #2100-065270, Teichmüller Spaces in Trace coordinates and Modular groups
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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