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Article Dans Une Revue Journal of topology Année : 2017

On codimension two embeddings up to link-homotopy

Jean-Baptiste Meilhan

Résumé

We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension 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 ≥ 3.
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Dates et versions

hal-01504996 , version 1 (10-04-2017)
hal-01504996 , version 2 (29-10-2017)

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Benjamin Audoux, Jean-Baptiste Meilhan, Emmanuel Wagner. On codimension two embeddings up to link-homotopy. Journal of topology, 2017, 10 (4), pp.1107-1123. ⟨10.1112/topo.12041⟩. ⟨hal-01504996v2⟩
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