Boundaries of deformation spaces of Kleinian groups
| Project/Area Number |
23540083
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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 | Nagoya University |
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Principal Investigator |
ITO Kentaro 名古屋大学, 多元数理科学研究科, 准教授 (00324400)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 双曲幾何 / クライン群 / リーマン面 |
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| Outline of Final Research Achievements |
I studied boundary behavior of deformation spaces of Kleinan groups. Especially, I studied the deformation space of the once-punctured torus group and made clear that how linear slices of traces close to 2 converge or not converge to the linear slice of trace 2 (Maskit slice). This is obtained from Bromberg's theory of non-local connectivity of the deformation space by using the trace coordinates. I also studied the deformation space of the twice-punctured torus groups. In addition, I started a research of distributions of totally geodesic planes in hyperbolic 3-manifolds. This corresponds to the study of actions of Kleinan groups on the 3-dimensional de-Sitter space.
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Report
(5 results)
Research Products
(15 results)
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[Presentation] Linear slices close to a Maskit slice
Author(s)
Kentaro Ito
Organizer
AMS Spring Central Sectional Meeting, Special Session on Analysis, Dynamics and Geometry In and Around Teichmuller Spaces
Place of Presentation
Iowa State University, USA
Related Report
Invited
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