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2003 The compression theorem III: applications
Colin Rourke, Brian Sanderson
Algebr. Geom. Topol. 3(2): 857-872 (2003). DOI: 10.2140/agt.2003.3.857


This is the third of three papers about the Compression Theorem: if Mm is embedded in Qq× with a normal vector field and if qm1, 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 [Partial differential relations, Springer–Verlag (1986); 2.4.5 C’] and the first two parts gave proofs. Here we are concerned with applications.

We give short new (and constructive) proofs for immersion theory and for the loops–suspension theorem of James et al and a new approach to classifying embeddings of manifolds in codimension one or more, which leads to theoretical solutions.

We also consider the general problem of controlling the singularities of a smooth projection up to C0–small isotopy and give a theoretical solution in the codimension 1 case.


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Colin Rourke. Brian Sanderson. "The compression theorem III: applications." Algebr. Geom. Topol. 3 (2) 857 - 872, 2003.


Received: 31 January 2003; Revised: 16 September 2003; Accepted: 24 September 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1032.57029
MathSciNet: MR2012956
Digital Object Identifier: 10.2140/agt.2003.3.857

Primary: 57R25, 57R27, 57R40, 57R42, 57R52
Secondary: 55P35, 55P40, 55P47, 57R20, 57R45

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.3 • No. 2 • 2003
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