Whitney-type Formula for Non-null-homotopic Curves on Aspherical Surfaces

2017/09/04 by Masayuki Yamasaki, Yamasaki, Masayuki
Mathematics · #57R42 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57R42

paper · pdf · doi:10.48550/arxiv.1709.00929

7 pages, 1 figure, Added two references and corrected many typos

openalex publication_date 2017/09/04 · openalex created_date 2017/09/15 · arxiv created 2017/09/28 · arxiv updated 2017/09/29 · openalex updated_date 2026/07/28

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.

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