Splitting sequences in Handel-Miller theory

We construct periodic train track splitting sequences for endperiodic surface homeomorphisms. These sequences combinatorialize laminations that are analogous to the invariant laminations of pseudo-Anosov mapping classes, but are also different in some essential ways. In doing this we port over some of the theory of layered veering triangulations to the setting of “depth 1 sutured manifolds.” This is part of an ongoing project aiming to prove a well-known but unpublished theorem of Gabai and Mosher concerning pseudo-Anosov flows and finite depth foliations in 3-manifolds. Joint with Chi Cheuk Tsang.