Computation of Nielsen and Reidemeister coincidence numbers for multiple maps

Abstract

Let $f_1,\ldots,f_k\colon M\to N$ be maps between closed manifolds, $N(f_1,\ldots,f_k)$ and $R(f_1,\ldots,f_k)$ be the Nielsen and the Reideimeister coincidence numbers, respectively. In this note, we relate $R(f_1,\ldots,f_k)$ with $R(f_1,f_2),\ldots,R(f_1,f_k)$. When $N$ is a torus or a nilmanifold, we compute $R(f_1,\ldots,f_k)$ which, in these cases, is equal to $N(f_1,\ldots,f_k)$.