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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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Geometric intersection numbers on a four-punctured sphere
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by Yungyen Chiang
Conform. Geom. Dyn. 1 (1997), 87-103
Published electronically: December 9, 1997


Let $\mathcal {G}_{4}$ be the space of all simple closed geodesics on the punctured sphere $\Sigma _{4}$. We construct an explicit homeomorphism of the completion of $\mathcal {G}_{4}$ onto a circle by using geometric intersection numbers. Also, we relate these geometric intersection numbers to trace polynomials of transformations corresponding to geodesics in $\mathcal {G}_{4}$ in a representation of $\pi _{1}(\Sigma _{4})$ into $PSL(2,\mathbf {C})$.
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Bibliographic Information
  • Yungyen Chiang
  • Affiliation: 4F No. 16 Chung Yang Rd., Taipei, Taiwan, Republic of China
  • Received by editor(s): April 28, 1997
  • Received by editor(s) in revised form: September 6, 1997
  • Published electronically: December 9, 1997
  • © Copyright 1997 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 1 (1997), 87-103
  • MSC (1991): Primary 30Fxx; Secondary 57-XX
  • DOI:
  • MathSciNet review: 1482943