no. 3
Cutting arcs for torus links and trees
[Découpages d’entrelacs toriques et de plombages positifs arborescents]
Misev, Filip1
1 Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Bulletin de la Société Mathématique de France, Tome 145 (2017) no. 3, pp. 575-602

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An, Dn, E6, E7 and E8) among all positive tree-like Hopf plumbings.

Parmi les entrelacs toriques, nous caractérisons ceux qui apparaissent comme entrelacs d’une singularité simple d’une courbe plane par la propriété que leurs surfaces fibres n’admettent qu’un nombre fini d’arcs de découpage qui préservent la fibration. La même propriété permet une caractérisation des arbres de Coxeter-Dynkin (i.e., An, Dn, E6, E7 et E8) parmi tous les plombages positifs arborescents.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.24033/bsmf.2747
Classification : 57M25, 32S55, 20F55
Keywords: Fibred knots and links, fibre surfaces, monodromy, cutting arcs, Hopf plumbing, singularities, Coxeter-Dynkin trees.
Mots-clés : Nœuds et entrelacs fibrés, surfaces fibrées, monodromie, arcs de découpage, plombage de Hopf, singularités, arbres de Coxeter-Dynkin.

Misev, Filip 1

1 Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland 
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Misev, Filip. Cutting arcs for torus links and trees. Bulletin de la Société Mathématique de France, Tome 145 (2017) no. 3, pp. 575-602. doi: 10.24033/bsmf.2747

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