Mathematical Sciences: Manifolds Which are Not Covering Spaces

赖特博士将研究的情况表明， 某些可收缩流形的维数大于或 等于3的不可能是非平凡的覆盖空间。 一个非常 罗伯特·迈尔斯（俄克拉荷马州）的一个美丽的三维结果 州立大学）表明，亏格一怀特黑德流形不能 非平凡地覆盖任何3-流形。 赖特博士的目标是 找到可以很容易地检查的条件， 开的可收缩n-流形不能是任何的覆盖空间 另一个流形。 这些条件表明，怀特黑德 任意亏格的流形（由Myers定义）不能是非- 平凡覆盖空间，即n维推广的 Whitehead流形不可能是非平凡覆盖空间， 并且Mazur可收缩四维流形的内部不能 是一个非平凡覆盖空间。 事实上，赖特博士希望他的 一种新的方法来产生一个重要的理解， 所有维度的可收缩开流形可以覆盖 空间.

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.