A Van Kampen type theorem for coincidences

The Nielsen coincidence theory is well understood for a pair of maps (f, g) : M-n --> N-n where M and N are compact manifolds of the same dimension greater than two. We consider coincidence theory of ct pair (f, g) : K --> N-n, where the complex K is the union of two compact manifolds of the same dimension as Nn. We define a number N(f, g : K-1, K-2) which is a homotopy invariant with respect to the maps. This number is certainly a lower bound for the number of coincidence points, and we prove a minimizing theorem with respect to this number. Finally, we consider the case where the target is a Jiang space and we obtain a nicer description of N(f, g : K-1, K-2) in terms of the Nielsen coincidence numbers of the maps restricted to the subspaces K-1, K-2. (C) 2000 Elsevier Science B.V. AU rights reserved.