Abstract
We define a regular homotopy invariant of closed curves on a surface, and give a formula for the rotation number of closed curves on torus, which is analogous to the Whitney formula for planar curves. As an application, we show a necessary condition for a Gauss word to be realized on torus.
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Tanio, H., Kobayashi, O. Rotation numbers for curves on a torus. Geom Dedicata 61, 1–9 (1996). https://doi.org/10.1007/BF00149414
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DOI: https://doi.org/10.1007/BF00149414