---
abstract: 'A *multicurve* ${\operatorname{{\mathcal{C}}}}$ on a closed orientable surface is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. The Dehn twist $t_{{\operatorname{{\mathcal{C}}}}}$ about ${\operatorname{{\mathcal{C}}}}$ 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 $h^n  = t_{{\operatorname{{\mathcal{C}}}}}$. 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.'
address:
- |
    Department of Mathematics\
    Indian Institute of Science Education and Research Bhopal\
    Bhopal Bypass Road, Bhauri\
    Bhopal 462 066, Madhya Pradesh\
    India
- |
    Department of Mathematics\
    Indian Institute of Science Education and Research Bhopal\
    Bhopal Bypass Road, Bhauri\
    Bhopal 462 066, Madhya Pradesh\
    India
author:
- Kashyap Rajeevsarathy
- Prahlad Vaidyanathan
bibliography:
- 'ultimate\_version.bib'
title: Roots of Dehn Twists about Multicurves
---

Introduction
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For $g \geq 0$, let $S_g$ be the closed, orientable surface of genus $g$, and let $\text{Mod}(S_g)$ denote the mapping class group of $S_g$. By a *multicurve* ${\operatorname{{\mathcal{C}}}}$ 