Geometry & Topology 5 (2001) 399–429

DOI: 10.2140/gt.2001.5.399

arXiv: math.GT/9712235

Abstract

This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q×R with a normal vector field and if q-m≥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×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.

Keywords

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

Mathematical Subject Classification

Primary: 57R25

Secondary: 57R27, 57R40, 57R42, 57R52

References

Forward citations

Publication

Received: 25 January 2001
Revised: 2 April 2001
Accepted: 23 April 2001
Published: 24 April 2001
Proposed: Robion Kirby
Seconded: Yasha Eliashberg, David Gabai

Authors