Algebraic & Geometric Topology 10 (2010) 373–432

DOI: 10.2140/agt.2010.10.373

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.

Keywords

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

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M99

References

Publication

Received: 26 December 2008
Revised: 13 November 2009
Accepted: 19 November 2009
Published: 2 March 2010

Authors