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Fibered $3$-manifolds
and Veech groups
Christopher J Leininger, Kasra Rafi, Nicholas Rouse, Emily Shinkle and Yvon Verberne |
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Algebraic & Geometric Topology 25 (2025) 1897–1915
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Abstract |
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We study Veech groups associated to the pseudo-Anosov monodromies of fibers and foliations of a fixed hyperbolic 3-manifold. Assuming Lehmer’s conjecture, we prove that the Veech groups associated to fibers generically contain no parabolic elements. For foliations, we prove that the Veech groups are always elementary. |
Keywords
pseudo-Anosov, Veech group, fibered $3$-manifold
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Mathematical Subject Classification
Primary: 57K32
Secondary: 57K20
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References |
Publication
Received: 14 October 2023
Revised: 10 January 2024
Accepted: 28 January 2024
Published: 20 June 2025
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Authors |
| Christopher J Leininger | |
| Department of Mathematics Rice University Houston, TX United States |
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| Kasra Rafi | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| Nicholas Rouse | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Emily Shinkle | |
| Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States |
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| Yvon Verberne | |
| Department of Mathematics Western University London, ON Canada |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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