2016 Fiscal Year Final Research Report
The geometric and dynamical decomposition of the character variety of surface groups
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 |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Nara Women's University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2017-03-31
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Keywords | 双曲幾何学 |
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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Free Research Field |
位相幾何学
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