December 2022 MOVES ON CURVES ON NONORIENTABLE SURFACES
Ferihe Atalan, S. Öykü Yurttaş
Rocky Mountain J. Math. 52(6): 1957-1967 (December 2022). DOI: 10.1216/rmj.2022.52.1957

Abstract

Let Ng,n denote a nonorientable surface of genus g with n punctures and one boundary component. We give an algorithm to calculate the geometric intersection number of an arbitrary multicurve with so-called relaxed curves in Ng,n making use of measured π1-train tracks. The algorithm proceeds by the repeated application of three moves which take as input the measures of and produces as output a multicurve which is minimal with respect to each of the relaxed curves. The last step of the algorithm calculates the number of intersections between and the relaxed curves.

Citation

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Ferihe Atalan. S. Öykü Yurttaş. "MOVES ON CURVES ON NONORIENTABLE SURFACES." Rocky Mountain J. Math. 52 (6) 1957 - 1967, December 2022. https://doi.org/10.1216/rmj.2022.52.1957

Information

Received: 13 May 2021; Revised: 9 December 2021; Accepted: 11 January 2022; Published: December 2022
First available in Project Euclid: 28 December 2022

MathSciNet: MR4527002
zbMATH: 1517.57016
Digital Object Identifier: 10.1216/rmj.2022.52.1957

Subjects:
Primary: 57M50
Secondary: 57N16

Keywords: geometric intersection , multicurves , π1-train tracks

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

Vol.52 • No. 6 • December 2022
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