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

J. Scott Carter; Masahico Saito; Shin Satoh

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

J. Scott Carter·Masahico Saito·Shin Satoh

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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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J. Scott Carter, Masahico Saito, Shin Satoh. 2004-07-28. Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers. https://arxiv.org/abs/math/0407493

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