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We study the space of link maps, which are smooth maps from the disjointunion of manifolds P and Q to a manifold N such that the images of P and Q aredisjoint. We give a range of dimensions, interpreted as the connectivity of acertain map, in which the cobordism class of the "linking manifold" is enoughto distinguish the homotopy class of one link map from another.

A stable range description of the space of link maps