Mathematical Sciences: Manifolds Which are Not Covering Spaces

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Dr. Wright will be studying conditions which imply that certain contractible manifolds of dimensions greater than or equal to three cannot be non-trivial covering spaces. A very beautiful three-dimensional result of J. Robert Myers (Oklahoma State University) shows that genus one Whitehead manifolds cannot non-trivially cover any 3-manifold. Dr. Wright's objectives are to find conditions which can be easily checked which show that an open contractible n-manifold cannot be a covering space of any other manifold. These conditions will show that Whitehead manifolds (as defined by Myers) of arbitrary genus cannot be non- trivial covering spaces, that n-dimensional generalizations of the Whitehead manifolds cannot be non-trivial covering spaces, and that the interior of the Mazur contractible 4-manifold cannot be a non-trivial covering space. In fact, Dr. Wright expects his new approach to produce a significant understanding of which contractible open manifolds of all dimensions can be covering spaces.