Riemann surfaces and low dimensional manifolds
Project/Area Number |
26400095
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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 | Gakushuin University |
Principal Investigator |
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Co-Investigator(Renkei-kenkyūsha) |
Ashikaga Tadashi 東北学院大学, 工学部, 教授 (90125203)
Komori Yohei 早稲田大学, 教育総合科学学術院, 教授 (70264794)
Ohmoto Toru 北海道大学, 理学研究科, 教授 (20264400)
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Project Period (FY) |
2014-04-01 – 2018-03-31
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Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | リーマン面 / ドリーニュ・マンフォードコンパクト化 / オービフォールド / 結晶群 / 4次元多様体 / タイヒミュラー空間 / モジュライ空間 / カーブ複体 / 写像類群 / コンパクト化 |
Outline of Final Research Achievements |
It is known that the moduli space of Riemann surfaces admits a natural compactification called the Deligne-Mumford compactification (DM-compactification). The main result of the present research is that we explicitly constructed a "natural" atlas consisting of orbifold charts on the DM-compactification of moduli space. These charts are indexed by the simplices of Harvey's curve complex. As a byproduct of the result, we discovered that certain higher dimensional euclidean crystallographic groups are attached to those orbifold charts that are indexed by the simplices of the maximum dimension. The theoretical meaning of this attachment of crystallographic groups will be studied in the future.
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Report
(5 results)
Research Products
(18 results)
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[Presentation] Riemann surfaces and Crystallographic Groups2016
Author(s)
Yukio Matsumoto
Organizer
2016 Winter TAPU Workshop on Knots and Related Topics
Place of Presentation
College of Natural Sciences, Kyungpook National University, Daegu, Korea
Year and Date
2016-02-16
Related Report
Int'l Joint Research / Invited
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