Invariants of knots and 3-manifolds

结和 3 流形的不变量

基本信息

批准号：
17540073
负责人：
OHTSUKI Tomotada
金额：
$ 1.28万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540073/
关键词：
knot 3-manifold invariant 2ループ多項式量子不変量同変不変量

项目摘要

I organized researches on invariants of knots and 3-manifolds. I presented the 2-loop polynomial of a knot by using finite type invariants of degree * 4 of a spine of a Seifert surface of the knot, from the viewpoint that I regard the 2-loop polynomial of a knot as an "equivariant Casson invariant" of the infinite cyclic cover of the complement of the knot. Further, I studied equivariant quantum invariants of the infinite cyclic cover of the complement of a knot, which unify quantum invariants of finite covers branched along the knot. Further, I constructed invariants of knots from equivariant linking matrices of their surgery presentations, from the viewpoint of studying equivariant quantum U(1) invariant of the infinite cyclic covers of the complements of the knots. Furthermore, I formulated a perturbative invariant of a 3-manifold with the first Betti number 1 in a certain case, as the arithmetic perturbative expansion of quantum invariants of the 3-manifold.I organized a low-dimensional topology seminar, jointly with Kazuo Habiro, who is a co-investigator of this research. The speakers were Yoko Mizuma, Takahito Kuriya, Soeren Hansen, Alexander Stoimenow, Vladimir Turaev, Alexis Virelizier, Gwenael Massuyeau, Masamichi Takase, and their talks were on advanced topics in the area of invariants of knots and 3-manifolds. I think their talks were very good, from the viewpoint of joint researches between them and me and the co-investigator, and from the viewpoint of research interactions between them and young researchers such as graduate students.

我组织了关于结和3个manifolds的不变的研究。我通过使用有限型不变性 * 4的脊柱脊柱的有限型不变式来呈现结的2环多项式，从我认为打结的2环多项式作为“ ecasson dopariant variant novariant noviant， “结的无限循环盖。此外，我研究了一个结的无限循环盖的量子化量子不变，该覆盖物的补充是一个有限覆盖的量子不变的量子覆盖沿结的有限覆盖物。此外，我是通过在研究等量子量子u（1）无限循环覆盖物的无限循环盖的角度来构建了与他们手术表现的矩阵相关的矩阵的不变的。此外，我在某个情况下制定了一个3个模型的扰动不变，第一个betti数字为1，因为3- manifold.i的量子不变性的算术扰动扩展组织了一个低维拓扑，与Kazuo habiro habiro habiro habiro habiro habiro in ，他是这项研究的共同评估者。演讲者是Mizuma Yoko Mizuma，Takahito Kuriya，Soeren Hansen，Alexander Stoimenow，Vladimir Turaev，Alexis virelizier，Gwenael Massuyeau，Masamichi Takase，他们的演讲及其在Knots of Knots of Knots of Knots of Knots and 3-Manifolds和3-Manifolds领域都在高级主题上。我认为，从我与我与共同研究者之间的共同研究的角度来看，他们的谈话非常好，从他们和研究生等年轻研究人员（例如研究生）之间的研究互动的角度来看。