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An application of non-positively curved cubings of alternating links


Authors: Makoto Sakuma and Yoshiyuki Yokota
Journal: Proc. Amer. Math. Soc. 146 (2018), 3167-3178
MSC (2010): Primary 57M25; Secondary 57M50
DOI: https://doi.org/10.1090/proc/13918
Published electronically: April 4, 2018
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Abstract: By using non-positively curved cubings of prime alternating link exteriors, we prove that certain ideal triangulations of their complements, derived from reduced alternating diagrams, are non-degenerate, in the sense that none of the edges is homotopic relative its endpoints to a peripheral arc. This guarantees that the hyperbolicity equations for those triangulations for hyperbolic alternating links have solutions corresponding to the complete hyperbolic structures. Since the ideal triangulations considered in this paper are often used in the study of the volume conjecture, this result has a potential application to the volume conjecture.


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Additional Information

Makoto Sakuma
Affiliation: Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 729-8526, Japan
Email: sakuma@hiroshima-u.ac.jp

Yoshiyuki Yokota
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397, Japan
Email: jojo@tmu.ac.jp

DOI: https://doi.org/10.1090/proc/13918
Received by editor(s): December 20, 2016
Received by editor(s) in revised form: June 12, 2017, and August 4, 2017
Published electronically: April 4, 2018
Additional Notes: The first author was partially supported by JSPS KAKENHI Grant Number 15H03620. The second author was partially supported by JSPS KAKENHI Grant Number 15K04878.
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society

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