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Conformal Geometry and Dynamics

ISSN 1088-4173



Geometric intersection numbers on a four-punctured sphere

Author: Yungyen Chiang
Journal: Conform. Geom. Dyn. 1 (1997), 87-103
MSC (1991): Primary 30Fxx; Secondary 57-XX
Published electronically: December 9, 1997
MathSciNet review: 1482943
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Abstract: 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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Additional 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
Article copyright: © Copyright 1997 American Mathematical Society