Stable Strata of Geodesics in Outer Space

Abstract

Abstract In this article, we propose an Outer space analog for the principal stratum of the unit tangent bundle to the Teichmüller space ${\mathcal{T}}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics in Teichmüller space determined by the principal stratum. We show that the analogous Outer space “principal” periodic geodesics share certain stability properties with the principal stratum geodesics of Teichmüller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichmüller space context.