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Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers
Author(s):
J.
Scott
Carter;
Masahico
Saito;
Shin
Satoh
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2779-2783.
MSC (2000):
Primary 57Q45;
Secondary 57Q35
Posted:
April 10, 2006
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Abstract:
We prove that a crossing change along a double point circle on a  -knot is realized by ribbon-moves for a knotted torus obtained from the  -knot by attaching a  -handle. It follows that any  -knots for which the crossing change is an unknotting operation, such as ribbon  -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:
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
Posted:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
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