Flows, growth rates, and the veering polynomial

Abstract For a pseudo-Anosov flow $\varphi $ without perfect fits on closed $3$ -manifold, Agol–Guéritaud produce veering triangulation $\tau the manifold M obtained by deleting singular orbits of . We show that can be realized in so its 2-skeleton is positively transverse to , and combinatorially defined graph $\Phi embedded uniformly codes precise sense. Together with these facts, we use modified version polynomial, previously introduced authors, compute growth rates after cutting along certain surfaces, thereby generalizing work McMullen fibered setting. These results are new even case where surface represents class boundary cone Our used study original manifold. Applications include counting defining continuous, convex entropy function ‘positive’ $H^1$ cut-open manifold, answering question Leininger about closure set all stretch factors arising as monodromies within single -manifold. This last application connects endperiodic automorphisms infinite-type surfaces their periodic points.