Volume 5, issue 1 (2001)

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The compression theorem I

Colin Rourke and Brian Sanderson

Geometry & Topology 5 (2001) 399–429

arXiv: math.GT/9712235

Abstract

This the first of a set of three papers about the Compression Theorem: if Mm is embedded in Qq × with a normal vector field and if q m 1, then the given vector field can be straightened (ie, made parallel to the given direction) by an isotopy of M and normal field in Q × .

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 2000
Primary: 57R25
Secondary: 57R27, 57R40, 57R42, 57R52
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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/