Whitney-type Formula for Non-null-homotopic Curves on Aspherical Surfaces
Geometric Topology
2017-09-29 v2
Abstract
In an earlier paper, I defined a new winding number of regular closed curves on complete euclidean/hyperbolic surfaces and showed that this winding number, together with the free homotopy class, determines the regular homotopy class. In this paper, I give a Whitney-type formula for the winding number of non-null-homotopic generic regular closed curves on surfaces with a complete euclidean or hyperbolic structure, generalizing the formula for curves on a torus by Tanio and Kobayashi.
Keywords
Cite
@article{arxiv.1709.00929,
title = {Whitney-type Formula for Non-null-homotopic Curves on Aspherical Surfaces},
author = {Masayuki Yamasaki},
journal= {arXiv preprint arXiv:1709.00929},
year = {2017}
}
Comments
7 pages, 1 figure, Added two references and corrected many typos