A Concordance Classification of p. 1. Homeomorphisms of Real Projective Space.
A well known theorem of Herman-Thurston states that the identity component of the group of diffeomorphisms of a boundaryless manifold is perfect and simple. We generalize this result to manifolds with boundary. Remarks on -diffeomorphisms are included.
It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing diffeomorphism group G is simple iff the foliation defined by [G,G] admits no proper minimal sets....