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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$
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by Thomas Gauglhofer and Klaus-Dieter Semmler PDF
Conform. Geom. Dyn. 9 (2005), 46-75 Request permission

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)
  • Email: thomas.gauglhofer@epfl.ch
  • Klaus-Dieter Semmler
  • Affiliation: EPFL SB IGAT GEOM, Bâtiment MA, Station 8, CH-1015 Lausanne (Switzerland)
  • Email: klaus-dieter.semmler@epfl.ch
  • 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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 9 (2005), 46-75
  • MSC (2000): Primary 32G15, 30F35; Secondary 11F06
  • DOI: https://doi.org/10.1090/S1088-4173-05-00106-2
  • MathSciNet review: 2133805