On the Haefliger-Thurston conjecture
Geometric Topology
2021-05-04 v3
Abstract
The classifying space for the framed Haefliger structures of codimension and class is -connected, for . The corollaries deal with the existence of foliations, with the homology and the perfectness of the diffeomorphism groups, with the existence of foliated products, and of foliated bundles.
Keywords
Cite
@article{arxiv.2103.13897,
title = {On the Haefliger-Thurston conjecture},
author = {Gael Meigniez},
journal= {arXiv preprint arXiv:2103.13897},
year = {2021}
}
Comments
This preprint is withdrawn, for an error occurs at the first line of page 10, while applying Lemma 1.1 to the microfoliation $\mathcal M$ of ${\mathcal G}_\alpha$. There is no global open neighborhood $U$ of the zero section in the total space of the normal bundle, such that ${\mathcal M}\vert U$ would be $C^r$ over the complement of $\alpha\times 0$, as asked in Lemma 1.1 (page 7, line 8)