Volume 10, issue 1 (2010)

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Stable concordance of knots in $3$–manifolds

Rob Schneiderman

Algebraic & Geometric Topology 10 (2010) 373–432

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.

$3$–manifold, Arf invariant, concordance, link invariant, stable concordance, stable embedding, Whitney disk, Whitney tower
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M99
Received: 26 December 2008
Revised: 13 November 2009
Accepted: 19 November 2009
Published: 2 March 2010
Rob Schneiderman
Department of Mathematics and Computer Science
Lehman College
City University of New York
New York, NY