(1) Oregon State University, Corvallis, OR, 97331, U.S.A
Abstract:
We give a classification of a specific family of seven-dimensional manifolds, the generalized Witten manifolds up to homeomorphism
and diffeomorphism. Using an approach suggested by J. Shaneson, we develop a modified surgery theory which fully classifies
these manifolds. In contrast to previous approaches, this surgery theory is designed to be more readily applicable to higher
dimensions. The family contains examples of manifolds which admit Einstein metrics and are homeomorphic but not diffeomorphic.
These particular manifolds occur naturally in differential geometry and are of great interest to both differential geometers
and physicists.