Abstract
The free splitting graph of a free group Fn with n≥2 generators is a hyperbolic Out(Fn)-graph which has a geometric realization as a sphere graph in the connected sum of n copies of S1×S2. We use this realization to construct submanifold projections of the free splitting graph into the free splitting graphs of proper free factors. This is used to construct for n≥3 a new hyperbolic Out(Fn)-graph. If n=3, then every exponentially growing element acts on this graph with positive translation length.
https://arxiv.org/abs/2403.18698