Geodesic
Macfarlane hyperbolic 3–manifolds
Quinn, Joseph1
1 Instituto de Matemáticas, Unidad Cuernavaca, UNAM, Cuernavaca, Mexico
Algebraic and Geometric Topology, Tome 18 (2018) no. 3, pp. 1603-1632

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We identify and study a class of hyperbolic 3–manifolds (which we call Macfarlane manifolds) whose quaternion algebras admit a geometric interpretation analogous to Hamilton’s classical model for Euclidean rotations. We characterize these manifolds arithmetically, and show that infinitely many commensurability classes of them arise in diverse topological and arithmetic settings. We then use this perspective to introduce a new method for computing their Dirichlet domains. We give similar results for a class of hyperbolic surfaces and explore their occurrence as subsurfaces of Macfarlane manifolds.

DOI : 10.2140/agt.2018.18.1603
Classification : 11R52, 57M27, 57M99
Keywords: Macfarlane space, quaternion hyperboloid, hyperbolic quaternions

Quinn, Joseph 1

1 Instituto de Matemáticas, Unidad Cuernavaca, UNAM, Cuernavaca, Mexico 
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Quinn, Joseph. Macfarlane hyperbolic 3–manifolds. Algebraic and Geometric Topology, Tome 18 (2018) no. 3, pp. 1603-1632. doi: 10.2140/agt.2018.18.1603

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