Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Non-simple links with tunnel number one

Author(s): Mario Eudave-Muñoz; Yoshiaki Uchida
Journal: Proc. Amer. Math. Soc. 124 (1996), 1567-1575.
MSC (1991): Primary 57M25
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

[BRZ]
M. Boileau, M. Rost and H. Zieschang, On Heegaard decompositions of torus knots exteriors and related Seifert fibred spaces, Math. Ann. 279 (1988), 553--581. MR 89a:57013

[E]
M. Eudave-Muñoz, On non-simple $3$-manifolds and $2$-handle addition, Topology and its applications 55 (1994), 131--152. MR 95e:57029

[J]
A. C. Jones, Composite two-generator links have a Hopf link summand, preprint.

[K]
T. Kobayashi, Structure of Haken manifolds with Heegaard splittings of genus two, Osaka J. Math. 21 (1984), 437--455. MR 85k:57011

[Mo]
Y. Moriah, A note on satellites and tunnel number, Kobe Journal of Math. 8 (1991), 73--79. MR 92m:57014

[M]
K. Morimoto, On composite tunnel number one links, preprint.

[MS]
K. Morimoto and M. Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991), 143--167. MR 92e:57015

[N]
F. H. Norwood, Every two generator knot is prime, Proc. Amer. Math. Soc. 86 (1982), 143--147. MR 83k:57005

[S]
M. Scharlemann, Tunnel number one knots satisfy the Poenaru conjecture, Topology and its applications 18 (1984), 235--258. MR 86e:57009

[T]
M. Takahashi, Two-bridge knots have Property P, Memoirs Am. Math. Soc. 29 (1981). MR 82f:57010

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M25

Retrieve articles in all Journals with MSC (1991): 57M25

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
Email: eudave@servidor.unam.mx

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
Email: uchida@math.s.kobe-u.ac.jp, yuchida@kszaoh3.kj.yamagata-u.ac.jp

DOI: 10.1090/S0002-9939-96-03393-X
PII: S 0002-9939(96)03393-X
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
Copyright of article: Copyright 1996, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google