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

 

Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers


Authors: J. Scott Carter, Masahico Saito and Shin Satoh
Journal: Proc. Amer. Math. Soc. 134 (2006), 2779-2783
MSC (2000): Primary 57Q45; Secondary 57Q35
Published electronically: April 10, 2006
MathSciNet review: 2213759
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Abstract: We prove that a crossing change along a double point circle on a $ 2$-knot is realized by ribbon-moves for a knotted torus obtained from the $ 2$-knot by attaching a $ 1$-handle. It follows that any $ 2$-knots for which the crossing change is an unknotting operation, such as ribbon $ 2$-knots and twist-spun knots, have trivial Khovanov-Jacobsson number.


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Additional Information

J. Scott Carter
Affiliation: Department of Mathematics, University of South Alabama, Mobile, Alabama 36688
Email: carter@jaguar1.usouthal.edu

Masahico Saito
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
Email: saito@math.usf.edu

Shin Satoh
Affiliation: Graduate School of Science and Technology, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan
Email: satoh@math.s.chiba-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08288-8
PII: S 0002-9939(06)08288-8
Keywords: Khovanov homology, 2-knot, ribbon-move, twist-spun knot, crossing change.
Received by editor(s): October 19, 2004
Received by editor(s) in revised form: April 14, 2005
Published electronically: April 10, 2006
Additional Notes: The first author was supported in part by NSF Grant DMS $#0301095$.
The second author was supported in part by NSF Grant DMS $#0301089$.
The third author was supported in part by JSPS Postdoctoral Fellowships for Research Abroad.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2006 American Mathematical Society