A class of manifolds covered by Euclidean space

Abstract

The following is the main result: Theorem 1. Suppose W n {W^n} is a PL manifold which has homotopy type K ( Π , 1 ) , W K(\Pi ,1),W has one end ∞ , π 1 \infty ,{\pi _1} is essentially constant at ∞ \infty , and the induced homomorphism π 1 ( ∞ ) → π 1 ( W ) {\pi _1}(\infty ) \to {\pi _1}(W) is an isomorphism. Then the universal cover of W W is PL homomorphic to R n {R^n} provided n ≥ 5 n \geq 5 .