Whitney towers in dimension 4 and Casson-Gordon style invariants of links

Abstract

In this thesis, 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 bound- ary, which was introduced by Cha. We also prove that the Blanchfield form and the Alexander polynomial of links in S3 give obstructions to height 3 Whitney tower/grope concordance. This generalizes the results of Hillman and Kawauchi.