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Conformal Geometry and Dynamics
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 | References | Similar Articles | Additional Information

Abstract: Let ${\cal G}_{4}$ be the space of all simple closed geodesics on the punctured sphere $\Sigma _{4}$. We construct an explicit homeomorphism of the completion of ${\cal G}_{4}$ onto a circle by using geometric intersection numbers. Also, we relate these geometric intersection numbers to trace polynomials of transformations corresponding to geodesics in ${\cal G}_{4}$ in a representation of $\pi _{1}(\Sigma _{4})$ into $PSL(2,\bold{C})$.


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Additional Information

Yungyen Chiang
Affiliation: 4F No. 16 Chung Yang Rd., Taipei, Taiwan, Republic of China

DOI: http://dx.doi.org/10.1090/S1088-4173-97-00020-9
PII: S 1088-4173(97)00020-9
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