Stable concordance of knots in 3–manifolds

Schneiderman, Rob

doi:10.2140/agt.2010.10.373

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Stable concordance of knots in $3$–manifolds

Rob Schneiderman

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 $S^{2} \times S^{2}$ . 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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M99

References

Publication

Received: 26 December 2008

Revised: 13 November 2009

Accepted: 19 November 2009

Published: 2 March 2010

Authors

Rob Schneiderman
Department of Mathematics and Computer Science Lehman College City University of New York New York, NY
http://comet.lehman.cuny.edu/schneiderman/

Volume 10, issue 1 (2010)