Obstruction theory and minimal number of coincidences for maps from a complex into a manifold

Abstract

The Nielsen coincidence theory is well understood for a pair of maps between $n$-dimensional compact manifolds for $n$ greater than or equal to three. We consider coincidence theory of a pair $(f,g)\colon K \to \mathbb N^n$, where $K$ is a finite simplicial complex of the same dimension as the manifold $\mathbb N^n$. We construct an algorithm to find the minimal number of coincidences in the homotopy class of the pair based on the obstruction to deform the pair to coincidence free. Some particular cases are analyzed including the one where the target is simply connected.