Homotopy classification of ribbon tubes and welded string links - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2014

Homotopy classification of ribbon tubes and welded string links

Jean-Baptiste Meilhan

Résumé

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper, we consider ribbon tubes, which are knotted annuli bounding ribbon 3-balls. We show how ribbon tubes naturally act on the reduced free group, and how this action classifies ribbon tubes up to link-homotopy, that is when allowing each tube component to cross itself. At the combinatorial level, this provides a classification of welded string links up to self-virtualization. This generalizes a result of Habegger and Lin on usual string links, and the above-mentioned action on the reduced free group can be refined to a general "virtual extension" of Milnor invariants. We also give a classification of ribbon torus-links up to link-homotopy. Finally, connections between usual, virtual and welded knotted objects are investigated.
Fichier principal
Vignette du fichier
wSL.pdf (565.64 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01017350 , version 1 (19-01-2016)
hal-01017350 , version 2 (05-02-2016)

Identifiants

Citer

Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan, Emmanuel Wagner. Homotopy classification of ribbon tubes and welded string links. 2014. ⟨hal-01017350v1⟩
459 Consultations
122 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More