Four-Ball Crossing Number

The Four-Ball Crossing Number, sometimes refered to as the "clasp 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 completed the computations for knots of 8 our fewer crossings. References are listed below.

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

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

B. Owens and S. Strle: Immersed disks, slicing numbers and concordance unknotting numbers (unpublished).