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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 S3 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
References
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