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Arithmeticity of hyperbolic $3$-manifolds containing infinitely many totally geodesic surfaces

Part of: Noncompact transformation groups Ergodic theory

Published online by Cambridge University Press:  22 April 2021

AMIR MOHAMMADI  and
GREGORII MARGULIS
AMIR MOHAMMADI*
Affiliation:
Department of Mathematics, The University of California, San Diego, CA92093, USA
GREGORII MARGULIS
Affiliation:
Mathematics Department, Yale University, PO Box 208283, New Haven, CT06520, USA (e-mail: gregorii.margulis@yale.edu)
*
e-mail: ammohammadi@ucsd.edu
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Abstract

We prove that if a closed hyperbolic $3$ -manifold M contains infinitely many totally geodesic surfaces, then M is arithmetic.

Keywords

hyperbolic 3-manifoldsarithmetic groupsgeodesic planes

MSC classification

Primary: 37A17: Homogeneous flows 22F30: Homogeneous spaces
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 3: Anatole Katok Memorial Issue Part 2: Special Issue of Ergodic Theory and Dynamical Systems , March 2022 , pp. 1188 - 1219
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

In memory of Anatole Katok

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