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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dehn surgeries on strongly invertible knots which yield lens spaces


Authors: Mikami Hirasawa and Koya Shimokawa
Journal: Proc. Amer. Math. Soc. 128 (2000), 3445-3451
MSC (2000): Primary 57N10, 57M25
Published electronically: May 18, 2000
MathSciNet review: 1676336
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Abstract:

In this article we show no Dehn surgery on nontrivial strongly invertible knots can yield the lens space $L(2p,1)$ for any integer $p$. In order to do that, we determine band attaches to $(2,2p)$-torus links producing the trivial knot.


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Additional Information

Mikami Hirasawa
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: hirasawa@math.sci.osaka-u.ac.jp

Koya Shimokawa
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan
Address at time of publication: Graduate School of Information Sciences, Tohoku University, Katahira Aoba-Ku, Sendai 980-8577, Japan
Email: simokawa@poisson.ms.u-tokyo.ac.jp, koya@math.is.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05417-4
PII: S 0002-9939(00)05417-4
Keywords: Dehn surgery, strongly invertible knot, lens space, banding
Received by editor(s): November 5, 1997
Received by editor(s) in revised form: January 8, 1999
Published electronically: May 18, 2000
Additional Notes: This research was partially supported by Fellowships of the Japan Society for the Promotion of Science for Japanese Junior Scientists.
Communicated by: Ronald Fintushel
Article copyright: © Copyright 2000 American Mathematical Society