| Project/Area Number |
23540085
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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 | Kyoto University |
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Principal Investigator |
FUJII MICHIHIKO 京都大学, 理学(系)研究科(研究院), 准教授 (60254231)
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| Co-Investigator(Kenkyū-buntansha) |
UE Masaaki 京都大学, 大学院・理学研究科, 教授 (80134443)
SATOH Takao 東京理科大学, 理学部, 講師 (70533256)
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| Co-Investigator(Renkei-kenkyūsha) |
KAWAZUMI Nariya 東京大学, 大学院・数理科学研究科, 准教授 (30214646)
SAITO Kyoji 東京大学, 数物連携宇宙研究機構, 主任研究員 (20012445)
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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 |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 幾何学 / トポロジー / 双曲幾何 / 離散群 / アルティン群 / 増大関数 / ブレイド群 / 二面体型 / 増大級数 / オートマトン / ピソ数 / 二面体群 / 双曲群 / 変形空間 / ２面体型 |
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| Research Abstract |
The head investigator Fujii obtained several results concerning pure Artin groups P of dihedral type. First, Fujii showed that the associated monoid is naturally embedded in P. Next, Fujii described a necessary and sufficient condition such that representatives of an element g of P are shotest among all representatives of g. Third, Fujii constructed a finite state automaton which accepts all the geodesic representatives of P, and obtained a rational function expression of the growth series for P. Moreover, Fujii showed that the growth rate of P is a Pisot number.
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