Anti-de Sitter strictly GHC-regular groups which are not lattices
Authors:
Gye-Seon Lee and Ludovic Marquis
Journal:
Trans. Amer. Math. Soc. 372 (2019), 153-186
MSC (2010):
Primary 20F55, 20F65, 20H10, 22E40, 51F15, 53C50, 57M50, 57S30
DOI:
https://doi.org/10.1090/tran/7530
Published electronically:
April 4, 2019
MathSciNet review:
3968766
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For , we exhibit examples of
strictly GHC-regular groups which are not quasi-isometric to the hyperbolic space
, nor to any symmetric space. This provides a negative answer to Question 5.2 in a work of Barbot et al. and disproves Conjecture 8.11 of Barbot-Mérigot [Groups Geom. Dyn. 6 (2012), pp. 441-483].
We construct those examples using the Tits representation of well-chosen Coxeter groups. On the way, we give an alternative proof of Moussong's hyperbolicity criterion (Ph.D. Thesis) for Coxeter groups built on Danciger-Guéritaud-Kassel's 2017 work and find examples of Coxeter groups such that the space of strictly GHC-regular representations of
into
up to conjugation is disconnected.
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Additional Information
Gye-Seon Lee
Affiliation:
Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Germany
Email:
lee@mathi.uni-heidelberg.de
Ludovic Marquis
Affiliation:
Université de Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
Email:
ludovic.marquis@univ-rennes1.fr
DOI:
https://doi.org/10.1090/tran/7530
Keywords:
Anti-de Sitter spaces,
Anosov representations,
quasi-Fuchsian groups,
Coxeter groups,
discrete subgroups of Lie groups
Received by editor(s):
August 30, 2017
Received by editor(s) in revised form:
January 19, 2018, and February 9, 2018
Published electronically:
April 4, 2019
Additional Notes:
The first author was supported by the European Research Council under ERC-Consolidator Grant 614733 and by DFG grant LE 3901/1-1 within the Priority Programme SPP 2026 “Geometry at Infinity”, and he acknowledges support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 “RNMS: Geometric structures and representation varieties” (the GEAR Network).
Article copyright:
© Copyright 2019
American Mathematical Society