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Submersions, fibrations and bundles
Author(s):
Gaël
Meigniez
Journal:
Trans. Amer. Math. Soc.
354
(2002),
3771-3787.
MSC (2000):
Primary 55R05, 55R10
Posted:
April 22, 2002
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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.
References:
-
- [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,
-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:
10.1090/S0002-9947-02-02972-0
PII:
S 0002-9947(02)02972-0
Received by editor(s):
September 1, 2001
Received by editor(s) in revised form:
October 20, 2001
Posted:
April 22, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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