Study on on properties and an extension of series and functions obtained from the quantum invariant of rational homology 3-shperes
| Project/Area Number |
25400094
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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 | Kyushu University |
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Principal Investigator |
TAKATA Toshie 九州大学, 数理学研究院, 准教授 (40253398)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 結び目・３次元多様体の量子不変量 / トポロジー / 量子不変量 / colored Jones polynomial / free energy / 量子摂動的不変量 |
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| Outline of Final Research Achievements |
We obtained a result that the second coefficient is presented by a constant multiple of the square root of the twisted Reidemeister torsion as N goes to the infinity in the asymptotic expansion of N colored Jones polynomial of a 2-bridge knots and SU(2) invariant of some hyperbolic 3-manifolds obtained by surgery along the figure-eight knot, by joint works with T. Ohtsuki.
We verified the slope conjecture for graph knots, i.e. knots whose Gromov volume vanish, by a joint work with K. Motegi.
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Report
(5 results)
Research Products
(13 results)
