Stable concordance of knots in 3-manifolds

Details Stable concordance of knots in 3-manifolds Stable concordance of knots in 3-manifolds

2008-12-26

arxiv.org/abs/0812.4696v1

Mathematics

Geometric Topology

59 pages, 28 figures

Scientific paper

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.

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