Constructing infinitely many geometric triangulations of the figure eight knot complement
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- by Blake Dadd and Aochen Duan PDF
- Proc. Amer. Math. Soc. 144 (2016), 4545-4555 Request permission
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.References
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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
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4545-4555
- MSC (2010): Primary 57M50, 57Q15
- DOI: https://doi.org/10.1090/proc/13076
- MathSciNet review: 3531201