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INTERSECTIONS OF MULTICURVES FROM DYNNIKOV COORDINATES

Part of: Special aspects of infinite or finite groups Topological manifolds Low-dimensional topology

Published online by Cambridge University Press:  03 May 2018

S. ÖYKÜ YURTTAŞ  and
TOBY HALL
S. ÖYKÜ YURTTAŞ
Affiliation:
Dicle University, Science Faculty, Mathematics Department, 21280, Diyarbakır, Turkey email saadet.yurttas@dicle.edu.tr
TOBY HALL*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK email T.Hall@liverpool.ac.uk
*
✉T.Hall@liverpool.ac.uk
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Abstract

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We present an algorithm for calculating the geometric intersection number of two multicurves on the $n$-punctured disk, taking as input their Dynnikov coordinates. The algorithm has complexity $O(m^{2}n^{4})$, where $m$ is the sum of the absolute values of the Dynnikov coordinates of the two multicurves. The main ingredient is an algorithm due to Cumplido for relaxing a multicurve.

Keywords

geometric intersectionmulticurvespunctured diskDynnikov coordinates

MSC classification

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20F36: Braid groups; Artin groups 57N16: Geometric structures on manifolds
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 149 - 158
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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