Abstract
A topological invariant of the geodesic laminations on a modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant is complete, i.e. the geodesic lamination can be recovered from the invariant. The continuous part of the invariant has geometric meaning of a slope of lamination on the surface.
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Notes
It is a tradition to reserve the term Chabauty topology for a topology on the set of all closed subgroups of a locally compact group. However, Canary, Epstein and Green (Canary et al. 1987) differ from the convention but point out that on metrizable space this is nothing but the Hausdorff topology.
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Acknowledgements
I am grateful to Samuil Kh. Aranson and Evgeny V. Zhuzhoma for an introduction to Weil’s problem. I thank the referee for a proofreading of the manuscript.
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Nikolaev, I.V. On a problem of A. Weil. Beitr Algebra Geom 59, 689–696 (2018). https://doi.org/10.1007/s13366-018-0383-9
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DOI: https://doi.org/10.1007/s13366-018-0383-9