4D Clasp Number

The 4D clasp number, sometimes refered to as the four-ball crossing number, of a knot is defined to be the minimum number of transverse self-intersection points of a smoothly immersed disk bounded by the knot in the 4-ball. It is bounded above by the unknotting number and below by the four-genus.

Brendan Owens and Saso Strle [3] completed the computations for knots of 8 or fewer crossings [3].


[1] Morimoto, K., "On the additivity of the clasp singularities," Kobe J. Math. 3 (1987), 179-185.

[2] Murakami H. and Yasuhara, A., "Four-genus and four-dimensional clasp number of a knot, Proc. Amer. Math. Soc. 128 (2000), 3693-3699.

[3] Owens, B. and Strle, S., "Immersed disks, slicing numbers and concordance unknotting numbers," Arxiv preprint.

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