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 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.
- Publication:
-
arXiv Mathematics e-prints
- 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
- E-Print:
- 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