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

Kim, Min Hoon

doi:10.2140/agt.2015.15.1813

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

Min Hoon Kim

Algebraic & Geometric Topology 15 (2015) 1813–1845

DOI: 10.2140/agt.2015.15.1813

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

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

Volume 15, issue 3 (2015)