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On unknotting numbers and four-dimensional clasp numbers of links


Author: Tomomi Kawamura
Journal: Proc. Amer. Math. Soc. 130 (2002), 243-252
MSC (2000): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-01-06000-2
Published electronically: May 7, 2001
MathSciNet review: 1855642
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Abstract:

In this paper, we estimate the unknotting number and the four-dimensional clasp number of a link, considering the greatest euler characteristic for an oriented two-manifold in the four-ball bounded by the link. Combining with a result due to Rudolph, we prove that an inequality stronger than the Bennequin unknotting inequality actually holds for any link diagram. As an application we show the equality conjectured by Boileau and Weber for a closed positive braid diagram.


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Additional Information

Tomomi Kawamura
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan
Email: kawamura@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-01-06000-2
Keywords: Unknotting number, 4-dimensional clasp number, Bennequin unknotting inequality
Received by editor(s): October 4, 1999
Received by editor(s) in revised form: May 12, 2000
Published electronically: May 7, 2001
Additional Notes: The author was partially supported by JSPS Research Fellowships for Young Scientists
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society

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