2020 Fiscal Year Final Research Report
Geometry of secondary characteristic classes
| Project/Area Number |
17K05243
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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 | Tohoku University (2018-2020)
Tokyo Institute of Technology (2017) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | トポロジー / 数理物理 / 特性類 / クラスター代数 / 数論トポロジー / 量子ダイログ関数 / 量子不変量 / 超対称ゲージ理論 |
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| Outline of Final Research Achievements |
Connecting topology to mathematical physics and number theory, we prove that specializations of cluster variables are identified with Alexander polynomials of 2-bridge knots in a joint work with Wataru Nagai, and get a result in arithmetic topology generalizing the reciprocity law about Riemann surfaces to 3-dimensional manifolds based on an analogy between foliated structures on 3-manifolds and number fields in a joint work with Junhyeong Kim, Masanori Morishita and Takeo Noda. Moreover, we introduce WRT functions, and prove that specializations of WRT functions to roots of unity are identified with WRT invariants for Seifert loops in a joint work with Hiroyuki Fuji, Kohei Iwaki and Hitoshi Murakami.
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| Free Research Field |
トポロジー，数理物理
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| Academic Significance and Societal Importance of the Research Achievements |
トポロジーと数理物理と数論をつなぐ新しい成果を得られたことにより，個々の分野の視点では今まで全く見えていなかったものが統一的に考えられるようになった．このことは新たな研究分野を創設することにもつながるものであり，分野を横断する研究を発展させることを今後も続けていきたい．
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