Speaker: Zlil Sela ，The Hebrew University of Jerusalem, Israel

Inviter: Rizos Sklinos 副研究员

Title: On rates of growth in groups

Language: English

Time & Venue: 2024.07.17 15:30-16:30 南楼N204

Abstract: A classical result of Jørgensen and Thurston shows that the set of volumes of finite volume complete hyperbolic 3-manifolds is a well-ordered subset of the real numbers of order type $w^w$;. Moreover, they showed that each volume can only be attained by finitely many isometry types of hyperbolic 3-manifolds.We will discuss a group-theoretic analogue of this result: If $\Gamma$ is a non-elementary hyperbolic group, then the set of exponential growth rates of $\Gamma$ is well-ordered, the order type is at least $w^w$, and each growth rate can only be attained by finitely many finite generating sets (up to automorphisms), and further generalizations of these results.The talk is intended to be for a wider audience. All the notions that are mentioned in the abstract will be explained. It is based on a joint work with K. Fujiwara (Kyoto University).