On codimension two embeddings up to link-homotopy

Abstract : 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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Journal of topology, Oxford University Press, 2017, 10 (4), pp.1107-1123. 〈http://onlinelibrary.wiley.com/doi/10.1112/topo.12041/full〉
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Dernière modification le : jeudi 18 janvier 2018 - 02:13:15

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  • HAL Id : hal-01504996, version 2
  • ARXIV : 1703.07999

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Benjamin Audoux, Jean-Baptiste Meilhan, Emmanuel Wagner. On codimension two embeddings up to link-homotopy. Journal of topology, Oxford University Press, 2017, 10 (4), pp.1107-1123. 〈http://onlinelibrary.wiley.com/doi/10.1112/topo.12041/full〉. 〈hal-01504996v2〉

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