Parametrizing Simple Closed Geodesy on Γ\h
نویسنده
چکیده
We exhibit a canonical geometric pairing of the simple closed curves of the degree three cover of the modular surface, Γ\H , with the proper single self-intersecting geodesics of Crisp and Moran. This leads to a pairing of fundamental domains for Γ with Markoff triples. The routes of the simple closed geodesics are directly related to the above. We give two parametrizations of these. Combining with work of Cohn, we achieve a listing of all simple closed geodesics of length within any bounded interval. Our method is direct, avoiding the determination of geodesic lengths below the chosen lower bound.
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