Counting pseudo-Anosovs as weakly contracting isometries

• 成果类型: Article
• 署名作者: Choi, Inhyeok
• 署名单位: Korea Institute for Advanced Study (KIAS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01358-5
• 发表日期: 2025
• 页码: 337-386
• 关键词: geometry; genericity; ELEMENTS; complex; braids; walks

摘要

We show that pseudo-Anosov mapping classes are generic in every Cayley graph of the mapping class group of a finite-type hyperbolic surface. Our method also yields an analogous result for rank-one CAT(0) groups and hierarchically hyperbolic groups with Morse elements. Finally, we prove that Morse elements are generic in every Cayley graph of groups that are quasi-isometric to (well-behaved) hierarchically hyperbolic groups. This gives a quasi-isometry invariant theory of counting group elements in groups beyond relatively hyperbolic groups.