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2018 Macfarlane hyperbolic $3$–manifolds
Joseph A Quinn
Algebr. Geom. Topol. 18(3): 1603-1632 (2018). DOI: 10.2140/agt.2018.18.1603

Abstract

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.

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Joseph A Quinn. "Macfarlane hyperbolic $3$–manifolds." Algebr. Geom. Topol. 18 (3) 1603 - 1632, 2018. https://doi.org/10.2140/agt.2018.18.1603

Information

Received: 4 March 2017; Revised: 15 January 2018; Accepted: 12 February 2018; Published: 2018
First available in Project Euclid: 26 April 2018

zbMATH: 06866408
MathSciNet: MR3784014
Digital Object Identifier: 10.2140/agt.2018.18.1603

Subjects:
Primary: 11R52, 57M27, 57M99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 3 • 2018
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