Triangulations and the stability theorem for foliations

Moulay-Tahar Benameur

Vol. 179 (1997), No. 2, 221–239

DOI: 10.2140/pjm.1997.179.221

Abstract

Let (M,F) be a smooth foliated manifold. We prove that there exists a triangulation of M such that each simplex is a distinguished chart for the foliation. This result enables us to give a complete geometric proof of the stability theorem. We also show that the relation between C^∗(M,F) and the C^∗-algebra of a regular covering, is a stability result.

Milestones

Received: 30 November 1995

Revised: 3 April 1996

Published: 1 June 1997