Tunnel number one knots, $m$-small knots and the Morimoto conjecture
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- by Guoqiu Yang, Xunbo Yin and Fengchun Lei PDF
- Proc. Amer. Math. Soc. 141 (2013), 4391-4399 Request permission
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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 4391-4399
- MSC (2010): Primary 57M99
- DOI: https://doi.org/10.1090/S0002-9939-2013-11700-4
- MathSciNet review: 3105881