New approach to discrete geometry --- capturing the shape of finite groups
| Project/Area Number |
24654016
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Keio University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 離散距離空間 / 離散群 / 剛性 / 離散集合 / 距離空間の埋め込み / 有限群 / 離散幾何学 |
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| Outline of Final Research Achievements |
The aim of this research was capturing the higher dimensional structure of discrete metric spaces and getting some rigidity results as applications of this structure. We could not obtain a satisfactory result describing the higher dimensional structure of discrete sets, however, using an observation and results obtained in the course of this research, we proved that certain random groups have strong fixed-point property for a wide class of nonpositively curved metric spaces. Also we gave some good estimates of nonlinear spectral gap for some embeddings of discrete metric spaces into nonpositively curved metric spaces.
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Report
(4 results)
Research Products
(11 results)
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[Book] 山辺の問題2013
Author(s)
小林治、芥川和雄、井関裕靖
Total Pages
75
Publisher
日本数学会
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