The θ p invariants of periodic 3-manifolds

Nafaa Chbili[1]

  • [1] Faculté des Sciences de Monastir, Département de Mathématiques, Boulevard de l'Environnement, Monastir 5000 (Tunisie)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 1135-1150
  • ISSN: 0373-0956

Abstract

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Let r ≥ 2 be an integer. A 3-manifold M is said to be r -periodic if and only if the group G = ℤ / r ℤ 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 .

How to cite

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Chbili, Nafaa. "Les invariants $\theta _p$ des 3-variétés périodiques." Annales de l’institut Fourier 51.4 (2001): 1135-1150. <http://eudml.org/doc/115937>.

@article{Chbili2001,
abstract = {Soit $r$ un entier $&gt;1$. Une 3-variété $M$ est dite $r$-périodique si et seulement si le groupe cyclique $G=\{\mathbb \{Z\}\}/r\{\mathbb \{Z\}\}$ agit semi-librement sur $M$ avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques $\theta _\{p\}$ pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.},
affiliation = {Faculté des Sciences de Monastir, Département de Mathématiques, Boulevard de l'Environnement, Monastir 5000 (Tunisie)},
author = {Chbili, Nafaa},
journal = {Annales de l’institut Fourier},
keywords = {periodic 3-manifold; periodic link; homology sphere; quantum invariants},
language = {fre},
number = {4},
pages = {1135-1150},
publisher = {Association des Annales de l'Institut Fourier},
title = {Les invariants $\theta _p$ des 3-variétés périodiques},
url = {http://eudml.org/doc/115937},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Chbili, Nafaa
TI - Les invariants $\theta _p$ des 3-variétés périodiques
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 1135
EP - 1150
AB - Soit $r$ un entier $&gt;1$. Une 3-variété $M$ est dite $r$-périodique si et seulement si le groupe cyclique $G={\mathbb {Z}}/r{\mathbb {Z}}$ agit semi-librement sur $M$ avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques $\theta _{p}$ pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.
LA - fre
KW - periodic 3-manifold; periodic link; homology sphere; quantum invariants
UR - http://eudml.org/doc/115937
ER -

References

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