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Bulletin of the American Mathematical Society

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Arithmetic hyperbolic reflection groups


Author: Mikhail Belolipetsky
Journal: Bull. Amer. Math. Soc. 53 (2016), 437-475
MSC (2010): Primary 22E40; Secondary 11F06, 11H56, 20H15, 51F15
DOI: https://doi.org/10.1090/bull/1530
Published electronically: March 29, 2016
MathSciNet review: 3501796
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Abstract: A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $ n$-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.


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Additional Information

Mikhail Belolipetsky
Affiliation: IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, Brazil
Email: mbel@impa.br

DOI: https://doi.org/10.1090/bull/1530
Received by editor(s): September 21, 2015
Published electronically: March 29, 2016
Dedicated: Dedicated to Ernest Borisovich Vinberg
Article copyright: © Copyright 2016 American Mathematical Society