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IMMERSIONS OF MANIFOLDS AND STABLE NORMAL BUNDLES

Li B

1987Mathematics被引 1

摘要

Let M~m and N~n be differentiable manifolds (m≤n), f: M~m→N~n any map, S_f the set of homotopy classes of monomorphisms of T(M)→T(N), and V_f the set of homotnpy classes of framings of the stable normal bundle of f with codimension n—m. It is proved that S_f corresponds to V_f in one-one fashion if the homotopy dimension of M≤n—2, and the correspondence commutes with the action of π_1(N~m, f). This allows us to calculate S_f easier (since there are known methods for calculating V_f), and obtain that the existence and classification of immersions of M in N depend only upon the stable tangent bundles of M and N, provided the homotopy dimension of M≤n—2.

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