摘要：Thorn-Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism φ：H^n(L：Z)→H^n(M：Z)to be realized by a map f:M→L of degree k for closed(n-1)-connected 2n-manifoldsM and L，n>1. A corollary is that each(n-1)-connected 2n-manifold admits selfmaps of degree larger than l，n>1. In the most interesting case of dimension 4． With the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms；in particular，there is a map f：M→L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M。

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