We consider smooth knottings of compact n-dimensional manifolds (not neces sarily orientable) in R (or S). We generalize to higher dimensions the classical notion of a knotting in general position with respect to projection. It is shown that any knotting is equivalent to one which is in general position with respect to pro jection. In higher dimensions, unlike classical knot theory, a generic projection is not necessarily an immersion. Thus we need to consider maps such that the set of non-immersion points is well behaved. The geometry of projections is exam ined and we use this information to show that any smooth knotting of an orientable n-manif old in R is smoothly isotopic to one whose projection into R is an im mersion. As corollary we obtain an elementary geometric proof that an orientable n-dimensional submanifold of R has trivial normal bundle. 1980 Mathematics Subject Classification: Primary 57R40, 57R42, 57R45, 57R52, 57Q45.
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