Geodesic
Fibered 3-manifolds and Veech groups
Leininger, Christopher J1 ; Rafi, Kasra2 ; Rouse, Nicholas3 ; Shinkle, Emily4 ; Verberne, Yvon5
1Department of Mathematics, Rice University, Houston, TX, United States
2Department of Mathematics, University of Toronto, Toronto, ON, Canada
3Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
4Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States
5Department of Mathematics, Western University, London, ON, Canada
Algebraic and Geometric Topology, Tome 25 (2025) no. 3, pp. 1897-1915
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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.

DOI : 10.2140/agt.2025.25.1897
Keywords: pseudo-Anosov, Veech group, fibered $3$-manifold

Leininger, Christopher J  1   ; Rafi, Kasra  2   ; Rouse, Nicholas  3   ; Shinkle, Emily  4   ; Verberne, Yvon  5

1 Department of Mathematics, Rice University, Houston, TX, United States
2 Department of Mathematics, University of Toronto, Toronto, ON, Canada
3 Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
4 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States
5 Department of Mathematics, Western University, London, ON, Canada 
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Leininger, Christopher J; Rafi, Kasra; Rouse, Nicholas; Shinkle, Emily; Verberne, Yvon. Fibered 3-manifolds and Veech groups. Algebraic and Geometric Topology, Tome 25 (2025) no. 3, pp. 1897-1915. doi: 10.2140/agt.2025.25.1897

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