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.

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

References in corpus (2)

• The compression theorem I
• The compression theorem III: applications

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• The compression theorem III: applications
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• The compression theorem II: directed embeddings
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• Refinements of the holonomic approximation lemma
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• Cobordism of singular maps
• Regular-equivalence of $2$-knot diagrams and sphere eversions
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• Kairvaire Problems in Stable Homotopy Theory
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