Rates of growth in hyperbolic (and other) groups

Speaker
Zlil Sela, HUJI
Date
27/03/2022 - 13:00 - 12:00Add to Calendar 2022-03-27 12:00:00 2022-03-27 13:00:00 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 ${\omega_0}^{\omega_0}$. 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. Seminar rm, Math Bldg 216 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Seminar rm, Math Bldg 216
Abstract

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

${\omega_0}^{\omega_0}$.

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.

Last Updated Date : 24/03/2022