Regularization and minimization of Haefliger structures of codimension one
Abstract
We prove the existence of a minimal (all leaves dense) foliation of codimension one, on every closed manifold of dimension at least 4 whose Euler characteristic is null, in every homotopy class of hyperplanes distributions, in every homotopy class of Haefliger structures, in every differentiability class, under the obvious embedding assumption. The proof uses only elementary means, and reproves Thurston's existence theorem in all dimensions. A parametric version is also established.
Keywords
Cite
@article{arxiv.0904.2912,
title = {Regularization and minimization of Haefliger structures of codimension one},
author = {Gael Meigniez},
journal= {arXiv preprint arXiv:0904.2912},
year = {2012}
}
Comments
This version is everywhere different from the previous one. The results are unchanged (except that dimension 3 is now excluded), but the proofs have been simplified. One works with Morse singularities, rather than with round ones. The "rolling up" of the holes has been simplified