Algebraic & Geometric Topology

Stable concordance of knots in $3$–manifolds

Rob Schneiderman

Full-text: Open access

Abstract

Knots and links in 3–manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato–Levine invariants and Milnor’s triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide obstructions to the existence of a singular concordance which can be homotoped to an embedding after stabilization by connected sums with S2×S2. Results include classifications of stably slice links in orientable 3–manifolds, stable knot concordance in products of an orientable surface with the circle and stable link concordance for many links of null-homotopic knots in orientable 3–manifolds.

Article information

Source
Algebr. Geom. Topol., Volume 10, Number 1 (2010), 373-432.

Dates
Received: 26 December 2008
Revised: 13 November 2009
Accepted: 19 November 2009
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882317

Digital Object Identifier
doi:10.2140/agt.2010.10.373

Mathematical Reviews number (MathSciNet)
MR2602841

Zentralblatt MATH identifier
1195.57034

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M99: None of the above, but in this section

Keywords
$3$–manifold Arf invariant concordance link invariant stable concordance stable embedding Whitney disk Whitney tower

Citation

Schneiderman, Rob. Stable concordance of knots in $3$–manifolds. Algebr. Geom. Topol. 10 (2010), no. 1, 373--432. doi:10.2140/agt.2010.10.373. https://projecteuclid.org/euclid.agt/1513882317


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