Geometry & Topology

Collar lemma for Hitchin representations

Gye-Seon Lee and Tengren Zhang

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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.

Article information

Geom. Topol., Volume 21, Number 4 (2017), 2243-2280.

Received: 22 December 2015
Revised: 10 July 2016
Accepted: 8 August 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]

hyperbolic surfaces convex real projective surfaces collar lemma Hitchin representations


Lee, Gye-Seon; Zhang, Tengren. Collar lemma for Hitchin representations. Geom. Topol. 21 (2017), no. 4, 2243--2280. doi:10.2140/gt.2017.21.2243.

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