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Constructing infinitely many geometric triangulations of the figure eight knot complement


Authors: Blake Dadd and Aochen Duan
Journal: Proc. Amer. Math. Soc. 144 (2016), 4545-4555
MSC (2010): Primary 57M50, 57Q15
DOI: https://doi.org/10.1090/proc/13076
Published electronically: May 6, 2016
MathSciNet review: 3531201
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Abstract: This paper considers ``geometric'' ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. As far as we know, this is the first construction of infinitely many geometric triangulations of a cusped hyperbolic 3-manifold. In contrast, our approach does not extend to the figure eight sister manifold, and it is unknown if there are infinitely many geometric triangulations for this manifold.


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Additional Information

Blake Dadd
Affiliation: School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia

Aochen Duan
Affiliation: School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia

DOI: https://doi.org/10.1090/proc/13076
Keywords: Hyperbolic 3-manifolds, geometric triangulations, Pachner moves
Received by editor(s): September 17, 2015
Received by editor(s) in revised form: December 22, 2015
Published electronically: May 6, 2016
Additional Notes: Both authors were supported by the Vacation Scholarship Program in the School of Mathematics and Statistics at the University of Melbourne.
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2016 American Mathematical Society