On commensurability of quadratic differentials

Abstract

We consider commensurability of quadratic differentials on surfaces. Each commensurability class has a natural order by the covering relation. We show that each commensurability class contains a unique (orbifold) element. We also discuss the relationship between commensurability of quadratic differentials and fibered commensurability, a notion introduced by Calegari-Sun-Wang.

5 pages. To appear in RIMS Kokyuroku Bessatsu. This is a preprint version. This paper was written and accepted while the author was in University of Tokyo