Sur des noeuds qui ne sont pas déterminés par leur complément et problèmes de chirurgie dans les variétés de dimension 3 / Yves Mathieu ; sous la responsabilité de Michel Domergue

Auteur principal : Mathieu, Yves, 1945-2005, AuteurAuteur secondaire : Domergue, Michel, Directeur de thèseAuteur secondaire collectivité : Université de Provence, Etablissement de soutenanceType de document : ThèseLangue : français.Pays: France.Éditeur : [S.l.] : [s.n.], 1990Description : 1 vol. (pagination multiple) ; 30 cmBibliographie : Bibliogr. .Sujet MSC : 57K31, Manifolds and cell complexes - Low-dimensional topology in specific dimensions, Invariants of 3-manifolds
57K10, Manifolds and cell complexes - Low-dimensional topology in specific dimensions, Knot theory
92C50, Biology and other natural sciences, Physiological, cellular and medical topics, Medical applications
97-02, Research exposition (monographs, survey articles) pertaining to mathematics education
Note de thèse: Thèse de doctorat es sciences mathématiques, mathématiques, 1990, Université de Provence
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Thèse de doctorat es sciences mathématiques mathématiques 1990 Université de Provence

A description of a geometric method is given, which constructs in every compact oriented 3-manifold V whose boundary is a torus (for example, V might be a solid torus) two knots which are inequivalent by homeomorphisms of V but which have (degree 1) homeomorphic complements, in contrast to the situation in the 3-sphere, where it is now known that knots are determined by their complements. See also a paper of D. Gabai [Topology 28, 1-6 (1989; Zbl 0678.57004), which completely answers the question for knots in the solid torus.

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