#### Volume 15, issue 3 (2015)

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

### Min Hoon Kim

Algebraic & Geometric Topology 15 (2015) 1813–1845
##### 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.

##### Keywords
link concordance, Whitney tower concordance, grope concordance, Casson–Gordon invariant
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57N70
##### Publication
Received: 8 July 2014
Revised: 20 October 2014
Accepted: 2 November 2014
Published: 19 June 2015
##### Authors
 Min Hoon Kim Department of Mathematics Pohang University of Science and Technology Gyungbuk 790-784 South Korea