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INTERSECTIONS OF MULTICURVES FROM DYNNIKOV COORDINATES

Published online by Cambridge University Press:  03 May 2018

S. ÖYKÜ YURTTAŞ
Affiliation:
Dicle University, Science Faculty, Mathematics Department, 21280, Diyarbakır, Turkey email [email protected]
TOBY HALL*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK email [email protected]
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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.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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