Study on Teichmuller modular groups through flat structures
| Project/Area Number |
26400151
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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 |
Basic analysis
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| Research Institution | Waseda University |
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Principal Investigator |
KOMORI YOHEI 早稲田大学, 教育・総合科学学術院, 教授 (70264794)
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| Project Period (FY) |
2014-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | リーマン面 / コクセター群 / サラム数 / 複素解析幾何学 / 複素解析幾何 / 国際研究者交流 |
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| Outline of Final Research Achievements |
Following the closed connection between Teichmuller modular subgroups and geometric Coxeter groups,
we constructed pseudo-Anosov mappings from Coxeter systems and considered their growth rates. Our Coxeter systems were obtained from affine Coxeter diagrams by adding one edge. Taking the double coverings of these diagrams, we showed that our Coxeter systems belong to hyperbolic class when the number of vertices of diagrams are less than or equal to 8, while they belong to higher rank class when the number of vertices of diagrams are more than or equal to 10. As an application of our result, we can construct a series of pseudo-Anosov mappings whose growth rates are 2-Salem numbers.
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| Academic Significance and Societal Importance of the Research Achievements |
曲面から曲面自身への自己同相写像の反復合成を曲面上の離散的な時間発展と思うと、曲面の種類及び同相写像の種類により複雑になる。特に種数が２以上の曲面における擬アノソフ写像は、伸びる方向と縮む方向に分解でき、トーラスの場合の双曲変換の類似になっている。この伸縮の割合を擬アノソフ写像の拡大率といい、その数論的性質など詳しく調べられている。
今回の研究では鏡映変換から定まるコクセター系という代数系を用いて、２サラム数という代数的整数を拡大率に持つ擬アノソフ写像を構成した。
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Report
(7 results)
Research Products
(26 results)
