| Project/Area Number |
26400088
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nara Women's University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
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| Keywords | 双曲幾何学 / ３次元多様体 / 低次元位相幾何学 / 指標多様体 |
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| Outline of Final Research Achievements |
The hyperbolic geometry is important in studying the geometry of two and three dimensional manifolds. To understand this geometry, we studied the character variety of the fundamental group of a surface. In particular, we defined a new kind of volume for closed three dimensional manifolds using hyperbolic geometry, and studied the basic structure of this invariant. Moreover, using CAT(0) cube complexes, we found conditions for infinite discrete groups, such as fundamental groups of manifolds, to became hyperbolic in the sense of Gromov.
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