Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications (Q6632135)

Veering triangulations were introduced by \textit{I. Agol} [Contemp. Math. 560, 1--17 (2011; Zbl 1335.57026)] in order to study mapping tori of pseudo-Anosov homeomorphisms (allowing certain degenerations of triangulations by allowing flat tetrahedra).\N\N``We study the strongly connected components of the flow graph associated to a veering triangulation, and show that the infinitesimal components must be of a certain form, which have to do with subsets of the triangulation which we call ``walls''. We show two applications of this knowledge: first, we fix a proof in the original paper by the first author [loc. cit.] which introduced veering triangulations; and second, give an alternated proof that veering triangulations induce pseudo-Anosov flows without perfect fits, which was initially proved by \textit{S. Schleimer} and \textit{H. Segerman} [``From veering triangulations to pseudo-Anosov flows and back again'', in preparation].''