  Given two compact n-dimensional manifolds in the smooth, piecewise linear or
topological categories, basic results of B. Mazur and others give simple
criteria for determining whether their products with Euclidean spaces of
sufficiently large dimension are isomorphic in the given category. This paper
studies such questions when the dimensions of the Euclidean space do not
satisfy such a condition, mainly for topological manifolds homotopy equivalent
to lens spaces with odd prime order fundamental groups. In particular, complete
information is obtained for homotopy lens spaces in most dimensions when the
Euclidean space is even dimensional. The proofs use basic techniques from
surgery theory and a variety of results from homotopy theory, including results
of Cohen, Moore and Neisendorfer related to finite exponents of certain
unstable homotopy groups.
