Diffeomorphism groups of connected sum of a product of spheres and classification of manifolds

Abstract

In [1] and [2] a classification of a manifold M of the type (n,p,1) was given where Hp(M)=Hn−p(M)=ℤ is the only non-trivial homology groups. In this paper we give a complete classification of manifolds of the type (n,p,2) and we extend the result to manifolds of type (n,p,r) where r is any positive integer and p=3,5,6,7mod(8).