geometry of automatic groups and dynamics of the boundary

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740049
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tohoku University (2012-2014); Kyoto University (2011)
• Principal Investigator: FUKAYA TOMOHIRO 東北大学, 理学(系)研究科(研究院), 講師 (40583456)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: Baum-Connes 予想 / 相対双曲群 / 境界 / 粗代数的位相幾何学 / 作用素環

Outline of Final Research Achievements

The Baum-Connes conjecture is one of the main topic of noncommutative geometry. We study its non-equivariant version, the coarse Baum-Connes conjecture. We proved that relatively hyperbolic groups satisfy the conjecture, under appropriate assumptions on parabolic subgroups. We also constructed a boundary for product of metric spaces. As application, we proved that the product of CAT(0)-groups, relatively hyperbolic groups, and polycyclic groups satisfy the conjecture.

Free Research Field

coarse geometry, geometric group theory