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From loom spaces to veering triangulations

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arxiv 2108.10264 v3 pith:UMSQBLMM submitted 2021-08-23 math.GT math.DS

Saul Schleimer , Henry Segerman This is my paper · ORCID
classification math.GTmath.DS
keywords spacesassociatedloomveeringtriangulationtriangulationscanonicallyeritaud
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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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  1. Heegaard Floer theory and pseudo-Anosov flows I: Generators and categorification of the zeta function

    math.GT 2025-04 conditional novelty 8.0 of 10

    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.

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