6533b825fe1ef96bd1281f67
RESEARCH PRODUCT
On codimension two embeddings up to link-homotopy
Emmanuel WagnerJean-baptiste MeilhanBenjamin Audouxsubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsHomotopy010102 general mathematicsClosure (topology)Geometric Topology (math.GT)CodimensionMSC: 57Q45 (primary); 57M27; 57Q35 (secondary)01 natural sciencesMathematics::Geometric TopologyMathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesRibbonKey (cryptography)FOS: Mathematics010307 mathematical physicsGeometry and Topology0101 mathematicsLink (knot theory)Mathematicsdescription
We consider knotted annuli in 4-space, called 2-string-links, which are knotted surfaces in codimension two that are naturally related, via closure operations, to both 2-links and 2-torus links. We classify 2-string-links up to link-homotopy by means of a 4-dimensional version of Milnor invariants. The key to our proof is that any 2-string link is link-homotopic to a ribbon one; this allows to use the homotopy classification obtained in the ribbon case by P. Bellingeri and the authors. Along the way, we give a Roseman-type result for immersed surfaces in 4-space. We also discuss the case of ribbon k-string links, for $k\geq 3$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-12-01 |