Let be an integer. A 3-manifold is said to be -periodic if and only if the group acts smoothly on with a circle as the set of fixed points. The aim of this paper is to study the invariants in the case where is an -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 and the invariant of the quotient 3-homology sphere . As an application it is shown that the Poincaré space is not the regular fold branched covering of , if is a prime congruent to modulo .
Soit un entier . Une 3-variété est dite -périodique si et seulement si le groupe cyclique agit semi-librement sur avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.
Mot clés : 3-variété périodique, entrelacs périodique, sphère d'homologie, invariants quantiques
Keywords: periodic 3-manifold, periodic link, homology sphere, quantum invariants
Chbili, Nafaa 1
@article{AIF_2001__51_4_1135_0, author = {Chbili, Nafaa}, title = {Les invariants $\theta _p$ des 3-vari\'et\'es p\'eriodiques}, journal = {Annales de l'Institut Fourier}, pages = {1135--1150}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {4}, year = {2001}, doi = {10.5802/aif.1848}, zbl = {0997.57031}, mrnumber = {1849218}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1848/} }
TY - JOUR AU - Chbili, Nafaa TI - Les invariants $\theta _p$ des 3-variétés périodiques JO - Annales de l'Institut Fourier PY - 2001 SP - 1135 EP - 1150 VL - 51 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1848/ DO - 10.5802/aif.1848 LA - fr ID - AIF_2001__51_4_1135_0 ER -
%0 Journal Article %A Chbili, Nafaa %T Les invariants $\theta _p$ des 3-variétés périodiques %J Annales de l'Institut Fourier %D 2001 %P 1135-1150 %V 51 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1848/ %R 10.5802/aif.1848 %G fr %F AIF_2001__51_4_1135_0
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. https://aif.centre-mersenne.org/articles/10.5802/aif.1848/
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