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