Collar lemma for Hitchin representations

Lee, Gye-Seon¹ ; Zhang, Tengren²

¹ Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
² Mathematics Department, California Institute of Technology, Mail Code 253-37, 1200 East California Boulevard, Pasadena, CA 91125, United States

Geometry & topology, Tome 21 (2017) no. 4, pp. 2243-2280.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.2243

Classification : 57M50, 30F60, 32G15
Keywords: hyperbolic surfaces, convex real projective surfaces, collar lemma, Hitchin representations

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