The compression theorem I

Rourke, Colin¹ ; Sanderson, Brian¹

¹ Mathematics Institute, University of Warwick, Coventry, CV5 7AL, United Kingdom

Geometry & topology, Tome 5 (2001) no. 1, pp. 399-429.

Résumé

This the first of a set of three papers about the Compression Theorem: if $M^m$ is embedded in $Q^q\times ℝ$ with a normal vector field and if $q-m\ge 1$, 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 $Q\times ℝ$.

The theorem can be deduced from Gromov’s theorem on directed embeddings 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.

Détail

DOI : 10.2140/gt.2001.5.399

Keywords: compression, embedding, isotopy, immersion, straightening, vector field

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