Decompositions of Manifolds Into Codimension One Submanifolds Compositio Mathematica, Tome 55, No 2 (1985), P
COMPOSITIO MATHEMATICA R. J. DAVERMAN Decompositions of manifolds into codimension one submanifolds Compositio Mathematica, tome 55, no 2 (1985), p. 185-207 <http://www.numdam.org/item?id=CM_1985__55_2_185_0> © Foundation Compositio Mathematica, 1985, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions gé- nérales d’utilisation (http://www.numdam.org/conditions). Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Compositio Mathematica 55 (1985) 185-207. 185 @ 1985 Martinus Nijhoff Publishers, Dordrecht. Printed in the Netherlands. DECOMPOSITIONS OF MANIFOLDS INTO CODIMENSION ONE SUBMANIFOLDS R.J. Daverman * 1. Introduction This paper investigates decompositions of boundaryless manifolds into closed, connected, codimension one submanifolds. It was inspired by recent work of V.T. Liem [22], with a related but distinct emphasis: typically the hypotheses in Liem’s results require that the decomposition elements have the shape of a codimension one sphere. It can be construed as an outgrowth of the same spirit leading to the studies by D.S. Coram [11] and by Coram and P.F. Duvall [13] of decompositions of S3 into simple closed curves. For example, in that spirit, because of the severe limitations on the decomposition elements within the source manifold M, one expects to discover a good deal of information about the decomposi- tion space, M/G. We prove that M/G is a 1-manifold, possible with boundary.
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