Computation of Nielsen numbers for maps of compact surfaces with boundary

In this paper we study the Nielsen number of a self-map f:M→M of a compact connected surface with boundary. Let G=π1(M) be the fundamental group of M which is a finitely generated free group. We introduce a new algebraic condition called “bounded solution length” on the induced endomorphism φ:G→G of f and show that many maps which have no remnant satisfy this condition. For a map f that has bounded solution length, we describe an algorithm for computing the Nielsen number N(f).