On the real secondary classes of transversely holomorphic foliations

Taro Asuke

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 3, page 995-1017
  • ISSN: 0373-0956

Abstract

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In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space H * ( WO 2 q ) of the real secondary classes to the space H * ( WU q ) 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.

How to cite

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Asuke, Taro. "On the real secondary classes of transversely holomorphic foliations." Annales de l'institut Fourier 50.3 (2000): 995-1017. <http://eudml.org/doc/75447>.

@article{Asuke2000,
abstract = {In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space $H^*(\{\rm WO\}_\{2q\})$ of the real secondary classes to the space $H^*(\{\rm WU\}_q)$ 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.},
author = {Asuke, Taro},
journal = {Annales de l'institut Fourier},
keywords = {foliations; transverse holomorphic structure; characteristic classes},
language = {eng},
number = {3},
pages = {995-1017},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the real secondary classes of transversely holomorphic foliations},
url = {http://eudml.org/doc/75447},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Asuke, Taro
TI - On the real secondary classes of transversely holomorphic foliations
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 3
SP - 995
EP - 1017
AB - In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space $H^*({\rm WO}_{2q})$ of the real secondary classes to the space $H^*({\rm WU}_q)$ 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.
LA - eng
KW - foliations; transverse holomorphic structure; characteristic classes
UR - http://eudml.org/doc/75447
ER -

References

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