Research on symmetries and mapping class groups on the surfaces in low-dimensional manifolds
Project/Area Number |
16K05156
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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 | Tokyo University of Science |
Principal Investigator |
Hirose Susumu 東京理科大学, 理工学部数学科, 教授 (10264144)
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Project Period (FY) |
2016-04-01 – 2023-03-31
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Project Status |
Completed (Fiscal Year 2022)
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Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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Keywords | 低次元トポロジー / 写像類群 / リーマン面 / 擬アノソフ同相写像 / 結び目 / 双曲多様体 / 分岐被覆空間 / 曲面結び目 / 周期的写像 / 代数曲線 / 3次元ハンドル体 / トポロジー / 3次元ハンドル体 |
Outline of Final Research Achievements |
We made several researches mainly on symmetries and mapping class groups on the surfaces embedded in 3 or 4-dimensional manifolds from the topological viewpoint. Especially, we obtained results on Dehn-twist presentations for the finite group actions on orientable closed surface of genus 3 or 4, Goeritz groups of bridge surfaces of knots in a 3-sphere, and branched virtual fibrations of 3-manifolds.
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Academic Significance and Societal Importance of the Research Achievements |
局所的に n 次元のユークリッド空間と同一視できる空間のことを n 次元多様体と呼ぶ.この空間を理解することは我々の住んでいる空間を理解するうえで欠かせないものであり,20世紀の後半には,次元 n が大きい場合について明解な理論が作られた.近年,特に n=3,4の場合の研究が急速に進展しており,本研究は,特に 2 次元多様体の上の写像に関する研究を通じて 3, 4 次元多様体の研究を推し進めるものである.
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Report
(8 results)
Research Products
(23 results)
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[Journal Article] A uniqueness of periodic maps on surfaces2016
Author(s)
Susumu Hirose, Yasushi Kasahara
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Journal Title
Journal of the Mathematical Society of Japan
Volume: 68
Issue: 4
Pages: 1777-1787
DOI
NAID
ISSN
0025-5645, 1881-1167, 1881-2333
Related Report
Peer Reviewed / Open Access / Acknowledgement Compliant
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