Abstract
This the first of a set of three papers about the Compression Theorem: if is embedded in with a normal vector field and if , then the given vector field can be straightened (ie, made parallel to the given direction) by an isotopy of and normal field in .
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.
Citation
Colin Rourke. Brian Sanderson. "The compression theorem I." Geom. Topol. 5 (1) 399 - 429, 2001. https://doi.org/10.2140/gt.2001.5.399
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