2014 Fiscal Year Final Research Report
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
|
| Keywords | 離散距離空間 / 離散群 / 剛性 |
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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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| Free Research Field |
微分幾何学
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