Whitney towers, gropes and Casson–Gordon style invariants of links

Abstract

In this paper, we prove a conjecture of Friedl and Powell that their Casson–Gordon type invariant of $2$–component links with linking number one is actually an obstruction to being height-$3.5$ Whitney tower/grope concordant to the Hopf link. The proof employs the notion of solvable cobordism of $3$–manifolds with boundary, which was introduced by Cha. We also prove that the Blanchfield form and the Alexander polynomial of links in $S^3$ give obstructions to height-$3$ Whitney tower/grope concordance. This generalizes the results of Hillman and Kawauchi.