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

Carter, J.; Saito, Masahico; Satoh, Shin

doi:10.1090/S0002-9939-06-08288-8

Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers
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by J. Scott Carter, Masahico Saito and Shin Satoh PDF

Proc. Amer. Math. Soc. 134 (2006), 2779-2783 Request permission

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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