Exotic limit sets of Teichm\"uller geodesics in the HHS boundary

Abstract

We answer a question of Durham, Hagen, and Sisto, proving that a Teichm\"uller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichm\"uller space. In fact, we prove that the limit set can be almost anything allowed by the topology.

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