Whitney towers, Gropes and Casson-Gordon style invariants of links

TL;DR

This paper proves that certain algebraic invariants like the Casson-Gordon invariant, Blanchfield form, and Alexander polynomial serve as obstructions to links being height 3.5 Whitney tower or grope concordant, advancing link concordance theory.

Contribution

It establishes new obstructions to Whitney tower/grope concordance using algebraic invariants, confirming a conjecture of Friedl and Powell and generalizing prior results.

Findings

Casson-Gordon invariant obstructs height 3.5 Whitney tower concordance.

Blanchfield form and Alexander polynomial obstruct height 3 Whitney tower concordance.

Proves Friedl and Powell's conjecture using solvable cobordism techniques.

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.