2015/06/04 by Kashyap Rajeevsarathy, Rajeevsarathy, Kashyap, Prahlad Vaidyanathan +1
Mathematics · #57M60 #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M60 #msc:57M99
paper · pdf · doi:10.48550/arxiv.1506.01534
31 pages, 6 figures
arxiv created 2015/06/04 · arxiv updated 2015/06/05
A multicurve \C on a closed orientable surface is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. The Dehn twist t\C about \C is the product of the Dehn twists about the individual curves. In this paper, we give necessary and sufficient conditions for the existence of a root of such a Dehn twist, that is, a homeomorphism h such that hn = t\C. We give combinatorial data that corresponds to such roots, and use it to determine upper bounds for n. Finally, we classify all such roots up to conjugacy for surfaces of genus 3 and 4.