#### Volume 21, issue 4 (2017)

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Collar lemma for Hitchin representations

### Gye-Seon Lee and Tengren Zhang

Geometry & Topology 21 (2017) 2243–2280
##### 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.

##### Keywords
hyperbolic surfaces, convex real projective surfaces, collar lemma, Hitchin representations
##### Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 30F60, 32G15