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