Study on actions of discrete groups on graphs and metrics on groups
| 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
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | 離散群 / 剛性 / エクスパンダー / 粗い幾何 / 幾何学 / グラフ / 固定点性質 / Kazhdanの性質（T) / エクスパンダーグラフ / Kazhdan 定数 / Kazhdan の性質 (T) / スペクトルギャップ / coarse 幾何 / エクスパンダー族 |
|---|
| 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.
|
Report
(5 results)
Research Products
(37 results)
