## Algebraic & Geometric Topology

### Stable concordance of knots in $3$–manifolds

Rob Schneiderman

#### 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
Revised: 13 November 2009
Accepted: 19 November 2009
First available in Project Euclid: 21 December 2017

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

#### 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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