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

Abstract

In [1] and [2] a classification of a manifoldMof the type(n,p,1)was given whereHp(M)=Hn−p(M)=ℤis 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)whereris any positive integer andp=3,5,6,7mod(8).