Rates of growth in hyperbolic (and other) groups
In the late 1970s W. Thurston proved that the countable set of volumes of
closed hyperbolic 3-manifolds is well-ordered, that only finitely many closed hyperbolic
3-manifolds can have the same volume, and that the ordinal of the set of these volumes is
We prove analogous results for the rates of growth of hyperbolic (and other) groups.
We study the countable set of rates of growth of a hyperbolic group with respect to all
its finite sets of generators, the countable set of rates of growth of all the finitely generated
subgroups of a hyperbolic group (with respect to all their finite generating sets), and the rates
of growth of all the finitely generated subsemigroups of a hyperbolic group.
Our results suggests a polynomial invariant for generating sets (and tuples) in (some) hyperbolic groups.
Joint work with Koji Fujiwara.
תאריך עדכון אחרון : 24/03/2022