Computing Nielsen numbers of surface homeomorphisms (Q1910437)

This work presents an algorithm to compute Nielsen numbers of surface homeomorphisms. It is based on the fact that \(N(h)\) (the Nielsen number of homeomorphism \(h)\) is the same as the number of fixed points of some homeomorphism \(f\) homotopic to \(h\). In order to get the number of fixed points of such a homeomorphism \(f\), one uses a handle structure of the surface and an algorithm due to Bestvina and Handle for finding a maximal reducing family \(C_h\). The final two algorithms obtained apply respectively to the case where the surface has nonempty boundary and the case where the surface is without boundary. One of them applies only for the case of nonempty boundary. Finally the author presents two examples which are very useful to understand the work.