Computing self-intersections of closed geodesics on finite-sheeted covers of the modular surface

Lehner, J.; Sheingorn, M.

doi:10.1090/S0025-5718-1985-0771045-7

Computing self-intersections of closed geodesics on finite-sheeted covers of the modular surface
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by J. Lehner and M. Sheingorn PDF

Math. Comp. 44 (1985), 233-240 Request permission

Abstract:

An algorithm is given for deciding whether a closed geodesic on a finite-sheeted cover of the modular surface has self-intersections; if it does, the algorithm gives them in the order they occur in traversing the geodesic. The following general result on geodesics is proved: any closed geodesic on a Riemann surface R can be lifted to a simple closed geodesic on some finite-sheeted cover of R. In the last two sections the connection with the stabilizer (under the modular group) of a Markov quadratic irrationality is discussed.

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