Computation of Nielsen numbers for maps of compact surfaces with boundary (Q861838)

Let \(M\) be a compact connected surface with boundary and \(f\) a self-map on \(M\). The author introduces a new algebraic condition called ``bounded solution length'' on the induced endomorphism \(\varphi: \pi _1 (M) \to \pi _1 (M) \) of \(f\) and shows that many maps which have no remnant satisfy this condition. For such a map \(f\) the author describes an algorithm for computing the Nielsen number \(N(f)\). Some illustrative examples are also given.