The spectrum of the growth rate of the tunnel number is infinite
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- by Kenneth L. Baker, Tsuyoshi Kobayashi and Yo’av Rieck PDF
- Proc. Amer. Math. Soc. 144 (2016), 3609-3618 Request permission
Abstract:
For any $\epsilon > 0$ we construct a hyperbolic knot $K \subset S^{3}$ for which $1 - \epsilon < \mathrm {gr}_t(K) < 1$. This shows that the spectrum of the growth rate of the tunnel number is infinite.References
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Additional Information
- Kenneth L. Baker
- Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
- MR Author ID: 794754
- Email: k.baker@math.miami.edu
- Tsuyoshi Kobayashi
- Affiliation: Department of Mathematics, Nara Women’s University, Kitauoya Nishimachi, Nara 630-8506, Japan
- Email: tsuyoshi@cc.nara-wu.ac.jp
- Yo’av Rieck
- Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 660621
- Email: yoav@uark.edu
- Received by editor(s): July 13, 2015
- Received by editor(s) in revised form: September 10, 2015
- Published electronically: February 2, 2016
- Additional Notes: The first and third authors would like to thank Nara Women’s University for their hospitality during the development of this article
The second author was supported by Grant-in-Aid for scientific research, JSPS grant number 00186751.
This work was partially supported by grants from the Simons Foundation (#209184 to the first author and #283495 to the third author) - Communicated by: Martin Scharlemann
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3609-3618
- MSC (2010): Primary 57M99, 57M25
- DOI: https://doi.org/10.1090/proc/12957
- MathSciNet review: 3503730