Topology
Thin presentation of knots in lens spaces and P 3 -conjecture
Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 937-940.

This Note concerns knots in a lens space L that produce S3 by Dehn surgery. We introduce the thin presentation of knots in L, with respect to a standard spine. We prove that among such knots, those having a thin presentation with only maxima, are 0-bridge or 1-bridge braids in L. In the case L=P 3 , we deduce that minimally braided knots in P 3 cannot yield S3 by Dehn surgery.

Cette Note concerne les nœuds d'un espace lenticulaire L qui produisent S3 par chirurgies de Dehn. Nous introduisons ici une présentation mince des nœuds de L, par rapport à une épine standard. Nous prouvons alors que parmi ces nœuds, ceux qui possèdent une présentation mince n'ayant que des maxima sont des 0 ou 1-tresses. Dans le cas où L=P 3 , nous déduisons que les nœuds minimalement tressés de P 3 ne peuvent produire S3 par chirurgie de Dehn.

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Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00218-8
Deruelle, Arnaud 1

1 Université de Provence, CMI, 39, rue Joliot Curie, 13453 Marseille cedex 13, France
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Deruelle, Arnaud. Thin presentation of knots in lens spaces and $ \mathbb{R}P^{3}$-conjecture. Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 937-940. doi : 10.1016/S1631-073X(03)00218-8. http://www.numdam.org/articles/10.1016/S1631-073X(03)00218-8/

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