On some spaces which are covered by a product space

Izu Vaisman

Annales de l'institut Fourier (1977)

  • Volume: 27, Issue: 1, page 107-134
  • ISSN: 0373-0956

Abstract

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In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the geometric structure of these spaces is clarified. Also, the morphisms of such spaces are characterized and indications regarding the homotopy and homology of the space are given. Finally one applies the obtained results to topological groups and to differentiable foliations. In this last case an alternative treatment of a class of foliations studied by L. Conlon (Trans. Amer. Math. Soc., 194 (1974), 79–102) and a part of a Cheeger-Gromoll-Lichnerowicz theorem (J. of Diff. Geom., 6 (1971), 47–94) are obtained.

How to cite

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Vaisman, Izu. "On some spaces which are covered by a product space." Annales de l'institut Fourier 27.1 (1977): 107-134. <http://eudml.org/doc/74305>.

@article{Vaisman1977,
abstract = {In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the geometric structure of these spaces is clarified. Also, the morphisms of such spaces are characterized and indications regarding the homotopy and homology of the space are given. Finally one applies the obtained results to topological groups and to differentiable foliations. In this last case an alternative treatment of a class of foliations studied by L. Conlon (Trans. Amer. Math. Soc., 194 (1974), 79–102) and a part of a Cheeger-Gromoll-Lichnerowicz theorem (J. of Diff. Geom., 6 (1971), 47–94) are obtained.},
author = {Vaisman, Izu},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {107-134},
publisher = {Association des Annales de l'Institut Fourier},
title = {On some spaces which are covered by a product space},
url = {http://eudml.org/doc/74305},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Vaisman, Izu
TI - On some spaces which are covered by a product space
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 1
SP - 107
EP - 134
AB - In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the geometric structure of these spaces is clarified. Also, the morphisms of such spaces are characterized and indications regarding the homotopy and homology of the space are given. Finally one applies the obtained results to topological groups and to differentiable foliations. In this last case an alternative treatment of a class of foliations studied by L. Conlon (Trans. Amer. Math. Soc., 194 (1974), 79–102) and a part of a Cheeger-Gromoll-Lichnerowicz theorem (J. of Diff. Geom., 6 (1971), 47–94) are obtained.
LA - eng
UR - http://eudml.org/doc/74305
ER -

References

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