Splittings of free groups from arcs and curves

Abstract

We show that the arc graph of $S_g^1$ is a coarse Lipschitz retract of the free splitting complex of $F_{2g}$. We also show that the arc and curve graph of $S_g^1$ is a coarse Lipschitz retract of both the cyclic splitting graph of $F_{2g}$ and the maximally cyclic splitting graph of $F_{2g}$.

16 pages

References in corpus (3)

• The free splitting complex of a free group I: Hyperbolicity
• Automorphisms of graphs of cyclic splittings of free groups
• Hyperbolicity of the Cyclic Splitting Complex