Coincidence theory for maps from a complex into a manifold

This work studies the coincidence theory of a pair of maps (f, g) from a complex K into a compact manifold of the same dimension. We define an index of a Nielsen coincidence class F which lies in some Z-module M(F) (varying with F). Then one can define the Nielsen coincidence number which is too weak to estimate μ(f, g). Finally we give a procedure to find a better lower bound for μ(f, g), where this is done for each Nielsen coincidence class. This relies strongly in the geometry of the complex K, and we can get different answers for two complexes K1, K2 of the same homotopy type.