Geometry & Topology

Whitney tower concordance of classical links

James Conant, Rob Schneiderman, and Peter Teichner

Full-text: Open access

Abstract

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato–Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4–ball bounded by a link in the 3–sphere. Applications include computation of the grope filtration and new geometric characterizations of Milnor’s link invariants.

Article information

Source
Geom. Topol., Volume 16, Number 3 (2012), 1419-1479.

Dates
Received: 4 February 2011
Revised: 28 May 2012
Accepted: 28 May 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732442

Digital Object Identifier
doi:10.2140/gt.2012.16.1419

Mathematical Reviews number (MathSciNet)
MR2967057

Zentralblatt MATH identifier
1257.57005

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 57Q60: Cobordism and concordance
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx]

Keywords
Whitney tower grope link concordance tree higher-order Arf invariant higher-order Sato–Levine invariant twisted Whitney disk

Citation

Conant, James; Schneiderman, Rob; Teichner, Peter. Whitney tower concordance of classical links. Geom. Topol. 16 (2012), no. 3, 1419--1479. doi:10.2140/gt.2012.16.1419. https://projecteuclid.org/euclid.gt/1513732442


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