In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space of the real secondary classes to the space of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also that Heitsch’s examples do not admit any transverse holomorphic structure.
Dans cet article nous étudions les classes caractéristiques secondaires réelles de feuilletages transversalement holomorphes. Nous définissons un homomorphisme de l’espace des classes secondaires réelles vers l’espace des classes secondaires complexes qui correspond à oublier la structure transversalement holomorphe. En utilisant cet homomorphisme nous montrons, par exemple, la décomposition de la classe de Godbillon-Vey en la partie imaginaire de la classe de Bott et la première classe de Chern du fibré normal complexe du feuilletage. Nous montrons aussi que des exemples de Heitsch n’admettent pas de structure transversalement holomorphe.
@article{AIF_2000__50_3_995_0, author = {Asuke, Taro}, title = {On the real secondary classes of transversely holomorphic foliations}, journal = {Annales de l'Institut Fourier}, pages = {995--1017}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {3}, year = {2000}, doi = {10.5802/aif.1782}, zbl = {0964.58018}, mrnumber = {2001i:58040}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1782/} }
TY - JOUR AU - Asuke, Taro TI - On the real secondary classes of transversely holomorphic foliations JO - Annales de l'Institut Fourier PY - 2000 SP - 995 EP - 1017 VL - 50 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1782/ DO - 10.5802/aif.1782 LA - en ID - AIF_2000__50_3_995_0 ER -
%0 Journal Article %A Asuke, Taro %T On the real secondary classes of transversely holomorphic foliations %J Annales de l'Institut Fourier %D 2000 %P 995-1017 %V 50 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1782/ %R 10.5802/aif.1782 %G en %F AIF_2000__50_3_995_0
Asuke, Taro. On the real secondary classes of transversely holomorphic foliations. Annales de l'Institut Fourier, Volume 50 (2000) no. 3, pp. 995-1017. doi : 10.5802/aif.1782. https://aif.centre-mersenne.org/articles/10.5802/aif.1782/
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