The compression theorem I

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 $q - m \geq 1$ , 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.

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/

Volume 5, issue 1 (2001)

Colin Rourke and Brian Sanderson