Rotation numbers for curves on a torus. (English) Zbl 0973.53507
Authors’ 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 a 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.
MSC:
53A04 | Curves in Euclidean and related spaces |
55M25 | Degree, winding number |
55N33 | Intersection homology and cohomology in algebraic topology |