Geometry & Topology

Collar lemma for Hitchin representations

Gye-Seon Lee and Tengren Zhang

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1508437641

Digital Object Identifier
doi:10.2140/gt.2017.21.2243

Mathematical Reviews number (MathSciNet)
MR3654108

Zentralblatt MATH identifier
1367.57010

Subjects
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]

Keywords
hyperbolic surfaces convex real projective surfaces collar lemma Hitchin representations

Citation

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. https://projecteuclid.org/euclid.gt/1508437641


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