2024/03/27 by Hamenstädt, Ursula, Hensel, Sebastian
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2403.18698
The free splitting graph of a free group Fn with n≥ 2 generators is a hyperbolic \rm 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 \rm Out(Fn)-graph. If n=3, then every exponentially growing element acts on this graph with positive translation length.