Foliations and groups of diffeomorphisms

John Mather has described a close relation between framed codimension-one Haefliger structures (these form a class of singular foliations), and the group of compactly supported diffeomorphisms of R 1 , with discrete topology [11], [12], [14]. In this announcement I will describe generalizations of his ideas to higher codimension Haefliger structures and groups of diffeomorphisms of arbitrary manifolds. See Haefliger [7] for a development of Haefliger structures and their classifying spaces.