Study on actions of discrete groups on graphs and metrics on groups

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800033
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year 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): 2013-04-01 – 2017-03-31
• 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 k-generated group" in certain sense is equipped with a natural topology that is metrizable and compact. For an infinite sequence of finite k-generated 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 k-generated 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 semi-continuous with respect to the convergence in the aforementioned topology.

Free Research Field

幾何学