2016 Fiscal Year Final Research Report
Study on actions of discrete groups on graphs and metrics on groups
Project/Area Number 
25800033

Research Category 
GrantinAid for Young Scientists (B)

Allocation Type  Multiyear Fund 
Research Field 
Geometry

Research Institution  Tohoku University 
Principal Investigator 
Mimura Masato 東北大学, 理学研究科, 助教 (10641962)

Project Period (FY) 
20130401 – 20170331

Keywords  離散群 / 剛性 / エクスパンダー / 粗い幾何 
Outline of Final Research Achievements 
For a fixed positive integer k, "the space of kgenerated group" in certain sense is equipped with a natural topology that is metrizable and compact. For an infinite sequence of finite kgenerated groups, we establish correspendence between group property of elements in this topological space appearing as an accumulation point and coarse geometric property of the infinite sequence. Moreover, we study on generalization of the Kazhdan constant, which is associated with Kazhdan's property (T). This quantity may be seen as a function on the space of kgenerated group. We generalize it to a general setting of fixed point property on a metric space, and under certain condition we prove that the defined function is lower semicontinuous with respect to the convergence in the aforementioned topology.

Free Research Field 
幾何学
