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Non-simple links with tunnel number one

Authors: Mario Eudave-Muñoz and Yoshiaki Uchida
Journal: Proc. Amer. Math. Soc. 124 (1996), 1567-1575
MSC (1991): Primary 57M25
MathSciNet review: 1328348
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Abstract: We determine all non-simple links which admit an unknotting tunnel, i.e. links which contain an essential annulus or torus in its exterior and have tunnel number one.

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Additional Information

Mario Eudave-Muñoz
Affiliation: Instituto de Matematicas, U.N.A.M. Circuito Exterior, Ciudad Universitaria, 04510 Mexico D. F. Mexico
Address at time of publication: Department of Mathematics, University of Texas, Austin, Texas 78712

Yoshiaki Uchida
Affiliation: Department of Mathematics, Kobe University, Rokko, Kobe 657, Japan
Address at time of publication: Department of Mathematical Sciences, Yamagata University, Yamagata 990, Japan

Keywords: Essential annulus or torus, non-simple link, unknotting tunnel
Received by editor(s): May 5, 1994
Additional Notes: The first author is grateful to the Osaka City University for its hospitality during the winter of 1993, where part of this work was done. The second author was partially supported by Grant-in-aid for Scientific Research, Ministry of Education, Science and Culture: A fellow of the Japan Society for the Promotion of Science for Japanese Junior Scientists
Communicated by: Ronald J. Stern
Article copyright: © Copyright 1996 American Mathematical Society

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