Embedding Coverings into Bundles with Applications

There are two parts to this paper. In the first part, we solve the problem of when a finite regular covering of a closed [italic]n-manifold M is homotopic to an embedding in an [italic]n-plane bundle over M. The results of the first part are used in the second part to obtain results on embedding [italic]n-manifold-like continua up to shape into 2n-space.