Multivariable Signatures, Genus Bounds, and 0.5-Solvable Cobordisms

Abstract

We refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the $4$-genus having their origins in the Murasugi–Tristram inequality, and at the same time extends previously known results about concordance invariance of the signature to a bigger set of allowed variables. Finally, we show that the multivariable signature and nullity are also invariant under $0.5$-solvable cobordism.