Iwip endomorphisms of free groups and fixed points of graph selfmaps

Abstract

In a paper from 2011, Jiang, Wang and Zhang studied the fixed points and fixed subgroups of selfmaps on a connected finite graph or a connected compact hyperbolic surface $X$. In particular, for any selfmap $f: X\to X$, they proved that a certain quantity defined in terms of the characteristic $\chr(f, \F)$ and the index $\ind(f, \F)$ of a fixed point class $\F$ of $f$ is bounded below by $2\chi(X)$, where $\chi(X)$ is the Euler characteristic of $X$. In this paper, we give a sufficient condition for when equality holds and hence we partially answer a question of Jiang, by studying iwip outer endomorphisms of free groups acting on stable trees.