: École d’Été 2018 - Teichmüller dynamics, mapping class groups and applications

Abstract

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by the Dynnikov coordinate system. In this talk we describe polynomial time algorithms for calculating the number of connected components of a multi curve, and the geometric intersection number of two multicurves on the n-punctured disk, taking as input their Dynnikov coordinates. This is joint work with Toby Hall

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