Geometric intersection numbers on a four-punctured sphere

Chiang, Yungyen

doi:10.1090/S1088-4173-97-00020-9

Geometric intersection numbers on a four-punctured sphere
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by Yungyen Chiang

Conform. Geom. Dyn. 1 (1997), 87-103

DOI: https://doi.org/10.1090/S1088-4173-97-00020-9

Published electronically: December 9, 1997

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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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