On codimension two embeddings up to link-homotopy

Benjamin Audoux; Jean-Baptiste Meilhan; Emmanuel Wagner

doi:10.1112/topo.12041

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arXiv · 1703.07999

On codimension two embeddings up to link-homotopy

Benjamin Audoux·Jean-Baptiste Meilhan·Emmanuel Wagner

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Abstract

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 $k\geq 3$.

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BibTeX RIS

Benjamin Audoux, Jean-Baptiste Meilhan, Emmanuel Wagner. 2017-10-29. On codimension two embeddings up to link-homotopy. https://doi.org/10.1112/topo.12041

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