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Transactions of the American Mathematical Society

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Submersions, fibrations and bundles


Author: Gaël Meigniez
Journal: Trans. Amer. Math. Soc. 354 (2002), 3771-3787
MSC (2000): Primary 55R05, 55R10
DOI: https://doi.org/10.1090/S0002-9947-02-02972-0
Published electronically: April 22, 2002
MathSciNet review: 1911521
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Abstract: When does a submersion have the homotopy lifting property? When is it a locally trivial fibre bundle? We establish characterizations in terms of consistency in the topology of the neighbouring fibres.


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  • [1] Cerf J., Topologie de certains espaces de plongements, Bull. Soc. Math. France 89 (1961), 227-380. MR 25:3543
  • [2] Epstein D.B.A., Curves on 2-manifolds and isotopies, Acta Mathematica 115 (1966), 83-107. MR 35:4938
  • [3] Ferry S., Alexander duality and Hurewicz fibrations, Trans. Amer. Math. Soc. 327, 1 (1991), 201-219. MR 91m:55015
  • [4] Haefliger A., Groupoïde d'holonomie et classifiants. in Structures transverses des feuilletages. Toulouse 1982, Astérisque 116 (1984), 70-97. MR 86c:57026a
  • [5] Hermann R., A sufficient condition that a mapping of Riemannian manifolds be a fiber bundle. Proc. Amer. Math. Soc. 11 (1960), 236-242. MR 22:3006
  • [6] Kirby R.C., The topology of 4-manifolds, Springer Lecture Notes in Mathematics 1374 (1989). MR 90j:57012
  • [7] Meigniez G., Submersions et fibrations localement triviales. C. R. Acad. Sci. Paris, 321, série I (1995), 1363-1365. MR 96m:57054
  • [8] Meigniez G., Sur le relèvement des homotopies. C. R. Acad. Sci. Paris, 321, série I (1995), 1497-1500. MR 97g:57008
  • [9] Palmeira C.F.B., Open manifolds foliated by planes, Ann. of Math. 107 (1978), 109-131. MR 58:18490
  • [10] Meigniez, G. Prolongement des homotopies, $Q$-variétés et cycles tangents, Ann. Inst. Fourier, Grenoble 47, 3 (1997), 945-965. MR 98h:57052
  • [11] Reinhart B.L., Foliated manifolds with bundle-like metrics, Ann. of Math. 69, 1 (1959), 119-132. MR 21:6004
  • [12] Siebenmann L., Thesis, Princeton U. (1965). See http://www.maths.ed.ac.uk/people/aar/ surgery/sieben.poly
  • [13] Stallings J., The piecewise linear structure of euclidian space, Proc. Cambridge Philos. Soc. 58 (1961), 481-488. MR 26:6945
  • [14] Weinstein A., Linearization of regular proper groupoids, preprint, Berkeley (2001). To appear in J. Inst. Math. Jussieu.

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Additional Information

Gaël Meigniez
Affiliation: Laboratoire de Mathématiques et d’Application des Mathématiques, Université de Bretagne Sud, Campus de Tohannic, Centre de recherche, F– 56017 Vannes Cedex, France
Email: Gael.Meigniez@univ-ubs.fr

DOI: https://doi.org/10.1090/S0002-9947-02-02972-0
Received by editor(s): September 1, 2001
Received by editor(s) in revised form: October 20, 2001
Published electronically: April 22, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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