Virtual Knot Cobordism and Bounding the Slice Genus

In this paper, we compute the slice genus for many low-crossing virtual knots. For instance, we show that 1295 out of 92,800 virtual knots with six or fewer crossings are slice, and that all but 248 of the rest are not slice. Key to these results are computations of Turaev’s graded genus, which we show extends to give an invariant of virtual knot concordance. The graded genus is remarkably effective as a slice obstruction, and we develop an …