A study on hyperbolic torsion polynomials and a DFJ conjecture for links
Project/Area Number |
17K05261
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Keio University |
Principal Investigator |
|
Project Period (FY) |
2017-04-01 – 2023-03-31
|
Project Status |
Completed (Fiscal Year 2022)
|
Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
Keywords | 双曲的トーション多項式 / DFJ予想 / 双曲絡み目 / 結び目群 / 双曲結び目 / 絡み目群 |
Outline of Final Research Achievements |
The purpose of this research was to extend a conjecture of Dunfield, Friedl and Jackson (we call it the DFJ conjecture for simplicity) on the genus and fiberedness of a hyperbolic knot in the 3-sphere and to comprehensively resolve it, including the original DFJ conjecture. A summary of the results is as follows. (1) We have formulated a generalized DFJ conjecture for a hyperbolic link in the 3-sphere rigorously, and in particular, have proved it for an infinite family of hyperbolic 2-bridge links. (2) As a stepping stone to prove the conjecture for a broader class of hyperbolic links, we have proved the original DFJ conjecture for an infinite family of hyperbolic 3-bridge knots.
|
Academic Significance and Societal Importance of the Research Achievements |
本研究では、空間内の結び目(ひも)が持つ基本的性質であるファイバー性と種数に関する予想について、それ自身の解決を目指すとともに、予想自体を一般化することで包括的に問題を解決することを目標としている。予想の適用範囲を広げることで問題の本質を明らかにし、俯瞰的な立場で問題の解決を図るという視点は、数学研究のみならず様々な場面で有効である。本研究成果は、低次元トポロジーの分野において、この観点からの新たな一例を与えるものとみなすことができる。
|
Report
(7 results)
Research Products
(28 results)