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Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3.
- Source :
-
Bulletin of the Brazilian Mathematical Society . Sep2012, Vol. 43 Issue 3, p347-373. 27p. - Publication Year :
- 2012
-
Abstract
- We consider singular foliations of codimension one on 3-manifolds, in the sense defined by André Haefliger as being Γ-structures. We prove that under the obvious linear embedding condition, they are Γ-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 ≥ 1. In particular, in dimension 3, this gives a very simple proof of Thurston's 1976 regularization theorem without using Mather's homology equivalence. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 43
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 80039881
- Full Text :
- https://doi.org/10.1007/s00574-012-0016-0