| Project/Area Number |
21540090
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
YOKOTA Yoshiyuki 首都大学東京, 大学院・理工学研究科, 准教授 (40240197)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 結び目 / ジョーンズ多項式 / 体積予想 / 双曲幾何 / 鞍点法 / カスプ / チャーン・サイモンズ不変量 |
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| Research Abstract |
The purpose of this research is to prove the volume conjecture for hyperbolic knots in 3-sphere, and to apply the results to find the ideal points of the deformation space of the hyperbolic structures of the knot complement and to find the shortest geodesic on the maximal torus.
The results of this research are to give a simple method to compute the Chern-Simons invariant of hyperbolic knot complements from knot diagrams, the proof of the volume conjecture for 5-crossing knots(joint work with R. Kashaev at University of Geneva), the proof of the volume conjecture for 6-crossing knots(joint work with T. Ohtsuki at Kyoto University), and to give a simple method to compute the cusp shape from the deformation of the potential function appearing in the integral expression of the colored Jones polynomial.
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