Stable concordance of knots in 3-manifolds

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 $S^2\times S^2$. 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.

59 pages, 28 figures

Cited by in corpus (6)

• Higher Order Intersections in Low-Dimensional Topology
• Whitney tower concordance of classical links
• Stably slice disks of links
• Relative genus bounds in indefinite four-manifolds
• Geometric Filtrations of Classical Link Concordance
• Finite type invariants of nullhomologous knots in 3-manifolds fibered over $S^1$ by counting graphs