Winding numbers of regular closed curves on aspherical surfaces

2016/02/08 by Masayuki Yamasaki, Yamasaki, Masayuki
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1602.02464

16 pages, 2 figures, AMS-LaTeX; omitted many figures, combined sections 2 and 3, omitted sections 6 and 7, corrected errors, added references

arxiv created 2017/08/09 · arxiv updated 2017/08/10

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.

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