The compression theorem I

Details The compression theorem I The compression theorem I

1997-12-09

arxiv.org/abs/math/9712235v3

Geom. Topol. 5(2001) 399-429

Mathematics

Geometric Topology

This is a shortened version of "The compression theorem": applications have been omitted and will be published as part III. Fo

Scientific paper

This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal field in Q X R. The theorem can be deduced from Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer-Verlag (1986); 2.4.5 C'] and is implicit in the preceeding discussion. Here we give a direct proof that leads to an explicit description of the finishing embedding. In the second paper in the series we give a proof in the spirit of Gromov's proof and in the third part we give applications.

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