Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of 𝖮𝗎𝗍(𝖥_{𝗇})

IF 2 4区数学 Q1 MATHEMATICS

Memoirs of the American Mathematical Society Pub Date : 2023-12-01 DOI:10.1090/memo/1454

M. Handel, L. Mosher

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引用次数: 1

Abstract

In this two part work we prove that for every finitely generated subgroup Γ > O u t ( F n ) \Gamma >{\mathsf {Out}}(F_n) , either Γ \Gamma is virtually abelian or H b 2 ( Γ ; R ) H^2_b(\Gamma ;{\mathbb {R}}) contains a vector space embedding of ℓ 1 \ell ^1 . The method uses actions on hyperbolic spaces. In Part I we focus on the case of infinite lamination subgroups Γ \Gamma —those for which the set of all attracting laminations of all elements of Γ \Gamma is an infinite set—using actions on free splitting complexes of free groups. In Part II we focus on finite lamination subgroups Γ \Gamma and on the construction of useful new hyperbolic actions of those subgroups.

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𝖮𝗎𝗍(𝖥_{𝗇})子群的双曲作用和第二有界同调

在这两部分的工作中，我们证明了对于每一个有限生成的子群Γ > Out (F n) \Gamma >{\mathsf {Out}}(F_n)， Γ \Gamma要么是虚阿贝尔的，要么是h2 (Γ;R) H^2_b(\Gamma;{\mathbb {R}})包含一个向量空间嵌入，它包含一个向量空间嵌入。该方法在双曲空间上使用动作。在第一部分中，我们主要讨论无限层叠子群Γ \Gamma的情况——其中Γ \Gamma的所有元素的所有吸引层叠的集合是一个无限集——利用自由群的自由分裂配合物上的作用。在第二部分中，我们重点讨论了有限层合子群Γ \Gamma以及这些子群的有用的新双曲作用的构造。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.