Seminar

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Given an endperiodic surface homeomorphism f, I will explain how to find a periodic splitting sequence of train tracks carrying f's positive Handel-Miller lamination. When f is atoroidal, this allows us to build an unstable "veering branched surface" in the compactified mapping torus of f. (This is analogous to Agol's construction of layered veering triangulations, which I will describe.) From this unstable veering branched surface, one can build an associated stable branched surface such that the two form a "dynamic pair."

The talk will be relatively self-contained and won't require knowledge of pseudo-Anosov flows or dynamic pairs. However, it is the second in a series describing the Gabai-Mosher construction of pseudo-Anosov flows associated to a finite depth foliation F of an atoroidal 3-manifold M. The Gabai-Mosher construction is inductive, where the induction is over the length of a sutured manifold hierarchy. The results in this talk comprise the basis step.

This is joint work with Chi Cheuk Tsang.

Veering branched surfaces from Handel-Miller theory