Collar lemma for Hitchin representations

Abstract

There is a classical result known as the collar lemma for hyperbolic surfaces. A consequence of the collar lemma is that if two closed curves $A$ and $B$ on a closed orientable hyperbolizable surface intersect each other, then there is an explicit lower bound for the length of $A$ in terms of the length of $B$, which holds for every hyperbolic structure on the surface. In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.