An approach to the superrigidity of infinite discrete groups via random groups

2017 Fiscal Year Final Research Report

• Project/Area Number: 25287013
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Keio University
• Principal Investigator: IZEKI Hiroyasu 慶應義塾大学, 理工学部(矢上), 教授 (90244409)
• Co-Investigator(Kenkyū-buntansha): 服部 広大 慶應義塾大学, 理工学部(矢上), 講師 (30586087) ; 勝良 健史 慶應義塾大学, 理工学部(矢上), 准教授 (50513298) ; 前田 吉昭 慶應義塾大学, 理工学部, 教授 (40101076)
• Co-Investigator(Renkei-kenkyūsha): NAYATANI Shin 名古屋大学, 大学院多元数理科学研究科, 教授 (70222180)
• Research Collaborator: KONDO Takefumi 鹿児島大学, 理学部
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 離散群 / 剛性 / 調和写像 / ランダム群

Outline of Final Research Achievements

The group is an algebraic object which also gives a description of symmetries of spaces. Some important and interesting groups often admits a property called "superrigidity", which we tried to understand as an extremal property among that involving infinite discrete groups. We could show that a fixed-point property, which should be considered to be an important aspect of superrigidity, is shared by finitely presented groups with overwhelming probability.

Free Research Field

数物系科学