A closed 3-manifold admits only finitely many pseudo-Anosov flows without perfect fits (and thus finitely many veering triangulations) up to isotopy.
From veering triangulations to dynamic pairs
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abstract
From a transverse veering triangulation (not necessarily finite) we produce a canonically associated dynamic pair of branched surfaces. As a key idea in the proof, we introduce the shearing decomposition of a veering triangulation.
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2026 1verdicts
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Finiteness of pseudo-Anosov flows without perfect fits
A closed 3-manifold admits only finitely many pseudo-Anosov flows without perfect fits (and thus finitely many veering triangulations) up to isotopy.