Abstract:We describe two connections between the theory of quasimorphisms and pseudo-Anosov flows without perfect fits on closed hyperbolic 3-manifolds. First we show that for every such flow $X$, there are quasimorphisms whose coarse restriction to each flowline of $\tilde{X}$ (the lifted flow in the universal cover) are uniform quasi-isometries to $\mathbb{R}$ -- such quasimorphisms are said to be *adapted* to $X$; and that the space of quasimorphisms $Q_X$ adapted to $X$ is an open convex cone in the space of all quasimorphisms on $\pi_1(M)$. Second, we obtain upper bounds on the exponential growth rate of closed orbits in such flows, both in the hyperbolic metric and in a word metric; quasimorphisms play a key role in obtaining the estimates in the second case.
From: Danny Calegari [view email]
[v1]
Fri, 12 Jun 2026 18:51:16 UTC (19 KB)
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