REGULARIZATION AND MINIMIZATION OF CODIMENSION-ONE HAEFLIGER STRUCTURES

Gael Gael Meigniez (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

On compact manifolds of dimensions 4 and more, we give a proof of Thurston's existence theorem for foliations of codimension one; that is, they satisfy some h-principle in the sense of Gromov. Our proof is an explicit construction not using the Mather homology equivalence. Moreover, the produced foliations are minimal, that is, all leaves are dense. In particular, there exist minimal smooth codimension-one foliations on every closed manifold of dimension at least 4 whose Euler characteristic is zero.

Mots clés: Haefliger’s Γ-structures; H-principle; Codimension 1 foliation; Minimal foliation

Domaines: Topologie géométrique [math.GT]

Gael Gael Meigniez. REGULARIZATION AND MINIMIZATION OF CODIMENSION-ONE HAEFLIGER STRUCTURES. 2016. ⟨hal-01449923v1⟩