[Un théorème de décomposition pour les bonnes complexifications]
Le but de cet article est de montrer qu’il existe des restrictions aux groupes fondamentaux que peuvent avoir les variétés admettant une bonne complexification, en démontrant le théorème suivant de décomposition, de type Cheeger–Gromoll : Toute variété fermée admettant une bonne complexification a un recouvrement fini , possédant un structure de fibré de base et de fibre ayant une bonne complexification et un premier nombre de Betti virtuel nul. On donne plusieurs applications de ce théorème aux variétés de dimension au plus .
The purpose of this paper is to produce restrictions on fundamental groups of manifolds admitting good complexifications by proving the following Cheeger-Gromoll type splitting theorem: Any closed manifold admitting a good complexification has a finite-sheeted regular covering such that admits a fiber bundle structure with base and fiber that admits a good complexification and also has zero virtual first Betti number. We give several applications to manifolds of dimension at most 5.
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Keywords: Good complexification, splitting theorem, affine variety, fundamental group, Geometrization theorem, virtual Betti number.
Mot clés : bonne complexification, théorème de décomposition, variété affine, groupe fondamental, théorème de géométrisation, nombre de Betti virtuel.
Biswas, Indranil 1 ; Mj, Mahan 1 ; Parameswaran, A. J. 1
@article{AIF_2016__66_5_1965_0,
author = {Biswas, Indranil and Mj, Mahan and Parameswaran, A. J.},
title = {A splitting theorem for good complexifications},
journal = {Annales de l'Institut Fourier},
pages = {1965--1985},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {5},
year = {2016},
doi = {10.5802/aif.3054},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3054/}
}
TY - JOUR AU - Biswas, Indranil AU - Mj, Mahan AU - Parameswaran, A. J. TI - A splitting theorem for good complexifications JO - Annales de l'Institut Fourier PY - 2016 SP - 1965 EP - 1985 VL - 66 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3054/ DO - 10.5802/aif.3054 LA - en ID - AIF_2016__66_5_1965_0 ER -
%0 Journal Article %A Biswas, Indranil %A Mj, Mahan %A Parameswaran, A. J. %T A splitting theorem for good complexifications %J Annales de l'Institut Fourier %D 2016 %P 1965-1985 %V 66 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3054/ %R 10.5802/aif.3054 %G en %F AIF_2016__66_5_1965_0
Biswas, Indranil; Mj, Mahan; Parameswaran, A. J. A splitting theorem for good complexifications. Annales de l'Institut Fourier, Tome 66 (2016) no. 5, pp. 1965-1985. doi : 10.5802/aif.3054. https://aif.centre-mersenne.org/articles/10.5802/aif.3054/
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