Cobordisms to weakly splittable links

Abstract

We show that if a link L with non-zero Alexander polynomial admits a locally flat cobordism to a `weakly m-split link', then the cobordism must have genus at least (m-1)/2. This generalises a recent result of J. Pardon.

11 pages, final version, to be published by the Proc. Amer. Math. Soc