Volume 5, issue 1 (2001)

Download this article
For printing
Recent Issues

Volume 29
Issue 7, 3345–3919
Issue 6, 2783–3343
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
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
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
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/