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Suppose TV is a closed ^-dimensional smooth manifold and M is a 2//-dimensional smooth manifold. In 1944, H. Whitney defined the self-intersection number for an immersion with normal crossings /: N -* M. We show that, if N is path-connected and the James-Thomas number of the normal bundle v(f) of / is greater than 1, then the self-intersection number is completely determined by the homotopy class of / and the normal bundle v(f).

Self-intersection number of immersions and enumeration of nonstable vector bundles