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 link 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.