Available in electronic format
Available in print format
Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

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
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

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, $Q$-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.

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 55R05, 55R10

Retrieve articles in all Journals with MSC (2000): 55R05, 55R10


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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google