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Tunnel number one knots, $ m$-small knots and the Morimoto conjecture


Authors: Guoqiu Yang, Xunbo Yin and Fengchun Lei
Journal: Proc. Amer. Math. Soc. 141 (2013), 4391-4399
MSC (2010): Primary 57M99
DOI: https://doi.org/10.1090/S0002-9939-2013-11700-4
Published electronically: August 16, 2013
MathSciNet review: 3105881
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Abstract: In the present paper, we show that the Morimoto Conjecture on the super additivity of the tunnel numbers of knots in $ S^3$ is true for knots $ K_1,K_2$ in $ S^3$ in which each $ K_i$ is either a tunnel number one or $ m$-small, $ i=1,2$. This extends two known results by Morimoto.


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Additional Information

Guoqiu Yang
Affiliation: School of Astronautics and Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
Email: gqyang@hit.edu.cn

Xunbo Yin
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
Email: jlxbyin@hit.edu.cn

Fengchun Lei
Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China
Email: ffcclei@yahoo.com.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11700-4
Keywords: Tunnel number, $m$-small, Morimoto Conjecture
Received by editor(s): July 15, 2011
Received by editor(s) in revised form: November 8, 2011, December 20, 2011, January 18, 2012, and February 8, 2012
Published electronically: August 16, 2013
Additional Notes: The first author was supported in part by two grants of NSFC (No. 11001065 and No. 11071106) and by two grants of HITQNJS (No. 2009.029 and No. 20100471066)
The second author was supported in part by a grant of NSFC (No. 11001065)
The third author was supported in part by a key grant of NSFC (No. 10931005)
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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