International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 17-33
doi:10.1155/S0161171287000036

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

Samuel Omoloye Ajala1,2

1School of Mathematics, The Institute for Advanced Study, Princeton 08540, New Jersey, USA
2Mathematics Department, University of Lagos, Akoka-Yaba, Lagos, Nigeria

Received 21 April 1986

Copyright © 1987 Samuel Omoloye Ajala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).