Translator Disclaimer
15 October 2019 The geometry of maximal representations of surface groups into SO0(2,n)
Brian Collier, Nicolas Tholozan, Jérémy Toulisse
Duke Math. J. 168(15): 2873-2949 (15 October 2019). DOI: 10.1215/00127094-2019-0052

Abstract

In this paper, we study the geometric and dynamical properties of maximal representations of surface groups into Hermitian Lie groups of rank 2. Combining tools from Higgs bundle theory, the theory of Anosov representations, and pseudo-Riemannian geometry, we obtain various results of interest. We prove that these representations are holonomies of certain geometric structures, recovering results of Guichard and Wienhard. We also prove that their length spectrum is uniformly bigger than that of a suitably chosen Fuchsian representation, extending a previous work of the second author. Finally, we show that these representations preserve a unique minimal surface in the symmetric space, extending a theorem of Labourie for Hitchin representations in rank 2.

Citation

Download Citation

Brian Collier. Nicolas Tholozan. Jérémy Toulisse. "The geometry of maximal representations of surface groups into SO0(2,n)." Duke Math. J. 168 (15) 2873 - 2949, 15 October 2019. https://doi.org/10.1215/00127094-2019-0052

Information

Received: 14 June 2017; Revised: 10 April 2019; Published: 15 October 2019
First available in Project Euclid: 30 September 2019

zbMATH: 07145323
MathSciNet: MR4017517
Digital Object Identifier: 10.1215/00127094-2019-0052

Subjects:
Primary: 20H10
Secondary: 14H60, 22E40, 53C50, 57M50, 58E12

Rights: Copyright © 2019 Duke University Press

JOURNAL ARTICLE
77 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.168 • No. 15 • 15 October 2019
Back to Top