Winding numbers of regular closed curves on aspherical surfaces
arXiv:1602.02464
Abstract
We define winding numbers of regular closed curves on surfaces with a nice euclidean or hyperbolic geometry. We prove that two regular closed curves are regularly homotopic if and only if they are freely homotopic and have the same winding number.
16 pages, 2 figures, AMS-LaTeX; omitted many figures, combined sections 2 and 3, omitted sections 6 and 7, corrected errors, added references