双曲群中的指数增长率（继 Koji Fujiwara 和 Zlil Sela 之后）
Exponential growth rates in hyperbolic groups (after Koji Fujiwara and Zlil Sela)
AI总结：
本文概述了 Fujiwara 和 Sela 的研究，证明非初等双曲群的指数增长率集合是良序的且序型至少为 $ω^ω$，每个增长率仅由有限多个生成集实现，建立了与双曲3-流形体积定理对应的群论结果。
摘要：
Jørgensen 和 Thurston 的经典结果表明，有限体积完备双曲 $3$-流形的体积集合是实数中序型为 $ω^ω$ 的良序子集；此外，每个体积只能由有限多种双曲 $3$-流形的等距类型实现。Fujiwara 和 Sela 建立了该结果的群论对应版本：若 $Γ$ 是非初等双曲群，则 $Γ$ 的指数增长率集合是良序的，序型至少为 $ω^ω$，且每个增长率只能由有限多个有限生成集（在自同构意义下）实现。在本次报告中，我们概述 Fujiwara 和 Sela 的这项工作并讨论相关结果。
英文摘要：
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~$ω^ω$; moreover, each volume can only be attained by finitely many isometry types of hyperbolic $3$-manifolds. Fujiwara and Sela established a group-theoretic companion of this result: If $Γ$ is a non-elementary hyperbolic group, then the set of exponential growth rates of~$Γ$ is well-ordered, the order type is at least~$ω^ω$, and each growth rate can only be attained by finitely many finite generating sets (up to automorphisms). In this talk, we outline this work of Fujiwara and Sela and discuss related results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
