Neat embeddings and immersions of compact manifolds with boundary (Q2640950)

\textit{R. Rigdon} and \textit{B. Williams} investigated the set of embeddings resp. immersions of closed smooth n-manifolds into \(S^{n+k}\) in ``Embeddings and immersions of manifolds'' [Geometric applications of homotopy theory I, Proc. Conf. Evanston 1977, Lect. Notes Math. 657, 423- 454 (1978; Zbl 0402.57018)]. They showed that in a metastable range of dimensions, these sets can be identified with certain subsets of (stable) homotopy groups of a suitable Thom complex and used this to compare embeddability resp. immersability of two manifolds that allow a degree 1 map which is sufficiently highly connected at the prime 2. The paper under review presents an analogous identification of the set of neat embeddings resp. immersions of a smooth n-manifold with boundary into \(D^{n+k}\) with certain (stable) relative homotopy groups. Applications are announced for a subsequent paper. An embedding \(M\subset D^{n+k}\) is called a neat embedding if \(\partial M\subset S^{n+k-1}\) and the normal vectors to \(\partial M\) point away from the boundary sphere.