On the Nielsen numbers of slide homeomorphisms on 3-manifolds

In this paper, we consider the fixed points of homeomorphisms of closed oriented reducible 3-manifolds. Up to an isotopy, we compute out the fixed point indices and fixed point coordinates for all isolated fixed point sets of homeomorphisms composed by two slides homeomorphism. An upper bound for the Nielsen numbers of these homeomorphisms is obtained. Finally, we shall show by some examples that Nielsen numbers of such kind of homeomorphisms can be arbitrarily large, although their Lefschetz numbers are zero.