Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3

Francois Laudenbach; Gael Gael Meigniez

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arXiv · 1108.2765

Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3

Francois Laudenbach·Gael Gael Meigniez

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Abstract

We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C^r, r at least 1. In particular, in dimension 3, this gives a very simple proof of Thurston's 1976 regularization theorem without using Mather's homology equivalence.

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BibTeX RIS

Francois Laudenbach, Gael Gael Meigniez. 2011-08-13. Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3. https://arxiv.org/abs/1108.2765

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