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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-06-08288-8

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