The theory of foliations of codimension greater than one

  title={The theory of foliations of codimension greater than one},
  author={William P. Thurston},
  journal={Commentarii Mathematici Helvetici},
  • W. Thurston
  • Published 1974
  • Mathematics
  • Commentarii Mathematici Helvetici
Controlled Mather-Thurston theorems
Classical results of Milnor, Wood, Mather, and Thurston produce flat connections in surprising places. The Milnor-Wood inequality is for circle bundles over surfaces, whereas the Mather-ThurstonExpand
Topologie des feuilles génériques
A smooth codimension-one foliation of the five-sphere by symplectic leaves
In 1969, in a landmark paper in the theory of foliations, Blai ne Lawson discovered the first example of a smooth codimension-one foliation of the sp hereS5 [8]. This example played a fundamentalExpand
Homotopy invariance of foliation Betti numbers
Foliation Betti numbers, introduced by Connes [C I], bear a striking formal similarity to the Betti numbers of a Galois covering space [A]. Both appear in a index theorem for DeRham complexes, andExpand
In this section we give some commentary on Thurston’s papers on foliations, denoted [F1] [F16] in the bibliography. We start by quoting his elegant definition of foliation [F11]. ”Given a largeExpand
On the uniqueness of the contact structure approximating a foliation
According to a theorem of Eliashberg and Thurston, a C-2-foliation on a closed 3-manifold can be C-0-approximated by contact structures unless all leaves of the foliation are spheres. Examples on theExpand
Existence of codimension-one foliations
A codimension-k foliation of a manifold Mn is a geometric structure which is formally defined by an atlas {qf: U. - Mn}, with U c Rn-k x R , such that the transition functions have the form 9pj(x, y)Expand
On the Haefliger-Thurston conjecture
The classifying space for the framed Haefliger structures of codimension q and class Cr is (2q − 1)-connected, for 1 ≤ r ≤ ∞. The corollaries deal with the existence of foliations, with the homologyExpand
Wrinkling of smooth mappings III. Foliations of codimension greater than one
This is the third paper in our Wrinkling saga (see [EM1], [EM2]). The first paper [EM1] was devoted to the foundations of the method. The second paper [EM2], as well as the current one are devoted toExpand
Noncritical holomorphic functions on Stein manifolds
We prove that every Stein manifold X of dimension n admits [(n+1)/2] holomorphic functions with pointwise independent differentials, and this number is maximal for every n. In particular, X admits aExpand


Foliations on 3-manifolds
Let M be a smooth manifold with tangent bundle TM. A k-plane field (or k-distribution) on M is a k-dimensional subbundle a of TM. Equivalently let a denote the section of the Grassmann bundle Gk(M)Expand
A Foliation for 3-Manifolds
Foliations of Odd-Dimensional Spheres
Codimension-One Foliations of Spheres
Homotopy and integrability
Manifolds — Amsterdam 1970
On Haefliger’s classifying space. I