A Compactly Generated Pseudo-Group which is Not Realizable

Gael Meigniez (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We exhibit a pseudogroup of smooth local transformations of the real line, which is compactly generated, but not realizable as the holonomy pseudogroup of a foliation of codimension 1 on a compact manifold. The proof relies on a description of all foliations with the same dynamic as the Reeb component.

Mots clés: Foliation; Pseudogroup; Compact generation

Domaines: Topologie géométrique [math.GT]

Gael Meigniez. A Compactly Generated Pseudo-Group which is Not Realizable. Journal of the Mathematical Society of Japan, 2010, 62 (4), pp.1205-1218. ⟨10.2969/jmsj/06241205⟩. ⟨hal-01436956⟩