The compression theorem I
Abstract
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 qm > 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, SpringerVerlag (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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.math/9712235
 arXiv:
 arXiv:math/9712235
 Bibcode:
 1997math.....12235R
 Keywords:

 Mathematics  Geometric Topology;
 57R25;
 57R27;
 57R40;
 57R42;
 57R52
 EPrint:
 This is a shortened version of "The compression theorem": applications have been omitted and will be published as part III. For a preliminary version of part III, see section 5 onwards of version 2 of this paper. This version (v3) is published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper14.abs.html