Les invariants θ p des 3-variétés périodiques
[The θ p invariants of periodic 3-manifolds]
Annales de l'Institut Fourier, Volume 51 (2001) no. 4, pp. 1135-1150.

Let r2 be an integer. A 3-manifold M is said to be r-periodic if and only if the group G=/r acts smoothly on M with a circle as the set of fixed points. The aim of this paper is to study the invariants θ p (M) in the case where M is an r-periodic 3-homology sphere. We use the regularity of the Kauffman bracket of periodic links introduced by Murasugi, to find a relationship between the invariant of M and the invariant of the quotient 3-homology sphere M ¯. As an application it is shown that the Poincaré space is not the regular r-fold branched covering of S 3 , if r is a prime congruent to ±1 modulo 5.

Soit r un entier >1. Une 3-variété M est dite r-périodique si et seulement si le groupe cyclique G=/r agit semi-librement sur M avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques θ p pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.

DOI: 10.5802/aif.1848
Classification: 57M27
Keywords: periodic 3-manifold, periodic link, homology sphere, quantum invariants
Chbili, Nafaa 1

1 Faculté des Sciences de Monastir, Département de Mathématiques, Boulevard de l'Environnement, Monastir 5000 (Tunisie)
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Chbili, Nafaa. Les invariants $\theta _p$ des 3-variétés périodiques. Annales de l'Institut Fourier, Volume 51 (2001) no. 4, pp. 1135-1150. doi : 10.5802/aif.1848. http://www.numdam.org/articles/10.5802/aif.1848/

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