Topological embeddings of topological manifolds into some Euclidean spaces (Q923434)

The main result in the paper is the following: ``Let W be a k-connected compact topological n-manifold with boundary, bdW a (k-1)-connected and \(1\leq k\leq n/2-1\) (bdW is 1-connected for \(k=1)\). Suppose that h is an integer, \(0\leq h\leq 2k\) and there exists an \((n-h-1)(>1)\)-dimensional normal microbundle \(\nu\) on W. Then (1) there exists a locally flat neat embedding of W into \(D^{2n-h}\) whose normal microbundle is isomorphic to \(\nu\oplus \epsilon\) where \(\epsilon\) is the trivial linear bundle; (2) there exists a locally flat embedding of W into \(S^{2n-h-1}\) whose normal bundle is isomorphic to \(\nu\).''