2010 Fiscal Year Final Research Report
Deformation spaces of Kleinian groups and conformal geometry
| Project/Area Number |
19740032
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Nagoya University |
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Principal Investigator |
ITO Kentaro Nagoya University, 大学院・多元数理科学研究科, 准教授 (00324400)
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| Project Period (FY) |
2007 – 2010
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| Keywords | クライン群 / 双曲幾何 / 離散群 / リーマン面 |
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| Research Abstract |
I studied the boundary behavior of deformation spaces of Kleinian groups. Especially, I obtained a necessary and sufficient condition in which a sequence of punctured torus groups converges/diverges. Therefore we obtained the whole picture of the self-bumping of the space of punctured torus groups. I also revealed the relation between the Maskit slice and the geometric limit of sequences of liner slices when the associated traces tend to 2. I also studied deformation spaces of 4-dimensional Kleinian groups.
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