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Given two maps f 1 , f 2 : M m −→ N n between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC(f 1 , f 2 ) of pathcomponents of the coincidence space of maps f ′ 1 , f ′ 2 where f ′ i is homotopic to f i , i = 1, 2 ? Approaching this question via normal bordism theory we define a lower bound N(f 1 , f 2 ) which generalizes the Nielsen number studied in classical fixed point and coincidence theory (where m = n). In at least three settings N(f 1 , f 2 ) turns out to coincide with MCC(f 1 , f 2 ): (i) when m < 2n − 2; (ii) when N is the unit circle; and (iii) when M and N are spheres and a certain injectivity condition involving James-Hopf invariants is satisfied. We also exhibit situations where N(f 1 , f 2 ) vanishes, but MCC(f 1 , f 2 ) is strictly positive.
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