Closed orbits of a pseudo-Anosov flow generate a sutured Heegaard Floer chain complex, and a new Z/2-grading on that complex categorifies the flow's zeta function.
From loom spaces to veering triangulations
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abstract
We introduce loom spaces, a generalisation of both the leaf spaces associated to pseudo-Anosov flows and the link spaces associated to veering triangulations. Following work of Gu\'eritaud, we prove that there is a locally veering triangulation canonically associated to every loom space, and that the realisation of this triangulation is homeomorphic to $\mathbb{R}^3$.
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Heegaard Floer theory and pseudo-Anosov flows I: Generators and categorification of the zeta function
Closed orbits of a pseudo-Anosov flow generate a sutured Heegaard Floer chain complex, and a new Z/2-grading on that complex categorifies the flow's zeta function.