New development of the research of Lefschetz fibrations by Teichmuller theory
| Project/Area Number |
23654024
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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 | Tokyo Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MIYACHI Hideki 大阪大学, 大学院・理学研究科, 准教授 (40385480)
ENDO Hisaaki 東京工業大学, 大学院・理工学研究科, 教授 (20323777)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | レフシェッツファイバー空間 / タイヒミュラー空間 |
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| Research Abstract |
Shiga obtained effective bounds of holomorphic families of Riemann surfaces, and also showed the rigidity and the finiteness of Teichmuller curves. In a joint work with Miyachi, Shiga studied relations of the holonomy and the slope inequality of Lefschetz fibrations.
Miyachi clarified the boundary behavior of the Teichmuller distance.
In a joint work with T. Mark and J. Van Horn-Morries, Endo found monodromy permutations for rational blow-downs and developed some method to study Lefschetz fibrations by using finite graphs.
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Report
(4 results)
Research Products
(80 results)
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[Presentation] Extremal length geometry of Teichmüller space2012
Author(s)
H. Miyachi
Organizer
Progress in Low-dimensional topology : Teichmüller theory and 3-manifold groups, Centre for Quantum Geometry of Moduli Spaces (QGM), Science and Technology
Place of Presentation
Aarhus University, Denmark
Year and Date
2012-08-11
Related Report
Invited
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[Presentation] Introduction to Teichmuller space
Author(s)
Hideki Miyachi
Organizer
Advanced School and discussion meeting on Knot theory and its application
Place of Presentation
Indian Institute of Science Education and Research, Mohali, Punjab, India
Related Report
Invited
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[Presentation] Isometry of Teichmuller space
Author(s)
Hideki Miyachi
Organizer
Advanced School and discussion meeting on Knot theory and its application
Place of Presentation
Indian Institute of Science Education and Research, Mohali, Punjab, India
Related Report
Invited
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[Presentation] Extremal length geometry of Teichmuller space
Author(s)
Hideki Miyachi
Organizer
Progress in Low-dimensional topology : Teichmuller theory and 3-manifold groups
Place of Presentation
Centre for Quantum Geometry of Moduli Spaces (QGM), Science and Technology, Aarhus University, Denmark
Related Report
Invited
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