Intersections of multicurves from Dynnikov coordinates

2017/11/02 by Yurttas, S. Öykü, Hall, Toby
#20F36 #57M50 #57N16 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1711.00895

Abstract

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(m²n⁴), 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.

Related

• Geometric intersection of curves on punctured disks
• Dynnikov coordinates on punctured torus
• Black holes in the Dynnikov Coordinate Plane
• Counting components of an integral lamination
• Intersection numbers in the curve complex via subsurface projections