Cycles of links and fixed points for orientation preserving homeomorphisms of the open unit disk

Michael Handel proved in Handel (1999) the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel's theorem to a wider class of cycles of links (Xavier 2012). In this paper we complete this topic describing exactly which are all the cycles of links forcing the existence of a fixed point.