Stable concordance of knots in 3–manifolds

Schneiderman, Rob¹

¹Department of Mathematics and Computer Science, Lehman College, City University of New York, New York, NY

Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 373-432

Résumé

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.

Détail

DOI : 10.2140/agt.2010.10.373

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

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