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Sur le rôle de la monodromie entière dans la topologie des singularités

Françoise MichelClaude Weber — 1986

Annales de l'institut Fourier

Nous considérons l’action de la monodromie sur l’homologie de la fibre de Milnor d’une singularité complexe. Cette action est plus compliquée que prévu : en effet nous montrons que, sur Z , elle n’est, en général, pas somme directe de modules cycliques. Nous donnons également des exemples prouvant que la monodromie rationnelle ne détermine pas la monodromie entière et que la monodromie entière ne détermine pas la topologie.

On malnormal peripheral subgroups of the fundamental group of a 3 -manifold

Pierre de la HarpeClaude Weber — 2014

Confluentes Mathematici

Let K be a non-trivial knot in the 3 -sphere, E K its exterior, G K = π 1 ( E K ) its group, and P K = π 1 ( E K ) G K its peripheral subgroup. We show that P K is malnormal in G K , namely that g P K g - 1 P K = { e } for any g G K with g P K , unless K is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in E K attached to T K which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental group of a...

A proof of Tait’s Conjecture on prime alternating - achiral knots

Nicola ErmottiCam Van Quach HonglerClaude Weber — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait’s Conjecture on alternating - achiral knots: Let K be a prime alternating - achiral knot. Then there exists a minimal projection Π of K in S 2 S 3 and an involution ϕ : S 3 S 3 such that: 1) ϕ reverses the orientation of S 3 ; 2) ϕ ( S 2 ) = S 2 ; 3) ϕ ( Π ) = Π ; 4) ϕ has two fixed points on Π and hence reverses...

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