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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

The compression theorem I

Colin Rourke and Brian Sanderson

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 Mm is embedded in Qq×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
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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
Colin Rourke
Mathematics Institute
University of Warwick
Coventry
CV5 7AL
United Kingdom
http://www.maths.warwick.ac.uk/~cpr/
Brian Sanderson
Mathematics Institute
University of Warwick
Coventry
CV5 7AL
United Kingdom
http://www.maths.warwick.ac.uk/~bjs/