Research on orbit equivalence through HNN extensions

2017 Fiscal Year Final Research Report

• Project/Area Number: 25800063
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: The University of Tokyo (2015-2017); Kyoto University (2013-2014)
• Principal Investigator: Kida Yoshikata 東京大学, 大学院数理科学研究科, 准教授 (90451517)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 離散群 / 軌道同型 / 測度付き亜群

Outline of Final Research Achievements

Our research interests lie in the orbit equivalence relation associated with a measure-preserving action of a countable group on a standard probability space, and we obtained results on its algebraic structure and relationship with the acting group. Among others, for the HNN extension of an infinite amenable group relative to an isomorphism between its finite index subgroups, including the Baumslag-Solitar groups, we showed stability of the orbit equivalence relation associated with its action and product structure of the kernel of the modular homomorphism. In addition, we studied characterization of stable groups with infinite center, and studied rigidity of actions of Torelli groups, Johnson kernels and surface braid groups.

Free Research Field

エルゴード群論