Intersections of multicurves from Dynnikov coordinates
Geometric Topology
2017-12-06 v2
Abstract
We present an algorithm for calculating the geometric intersection number of two multicurves on the -punctured disk, taking as input their Dynnikov coordinates. The algorithm has complexity , where 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
Cite
@article{arxiv.1711.00895,
title = {Intersections of multicurves from Dynnikov coordinates},
author = {S. Öykü Yurttas and Toby Hall},
journal= {arXiv preprint arXiv:1711.00895},
year = {2017}
}
Comments
9 pages. Corrected error in paragraph 1 about complexity of [2] and [9], with thanks to Mark Bell and Saul Schleimer