Connectivity of the Gromov boundary of the free factor complex (Q6191452)

Let \(F_{n}\) be a free group. A well-known analogue of the curve complex in the context of \(\mathrm{Out}(F_{n})\) is the free factor complex \(FF_{n}\). The Gromov hyperbolicity of \(FF_{n}\) was established by the first author and \textit{M. E. Feighn} in [Adv. Math. 256, 104--155 (2014; Zbl 1348.20028)]. The main result in this paper is Theorem 1.1: The Gromov boundary \(\partial FF_{n}\) of the free factor complex is path connected and locally path connected for \(n\) large enough. As a consequence the authors obtain the following coarse geometric property (see Corollary 1.2): \(FF_{n}\) is one-ended for \(n\) large enough.