低次元トポロジーの総合的研究

低维拓扑综合研究

• 批准号: 13440018
• 负责人: MURAKAMI Hitoshi
• 金额: $ 7.1万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440018/
• 关键词: knot; 3-manifold; quantum ivariant; lowdimensional topology; graph; 絡み目

The academic year 2001: We organized the yearlong Research Project 'Low-Dimensional Topology in the 21st Century' at the Research Institute for Mathematical Sciences, Kyoto UniversityIn this project we invited low-dimensional topologists from inside and outside Japan. We had about 50 visitors from overseas and we could exchange information and could discuss on various areas with many lectures. Consequently we could obtain new aspects on many areas in low-dimensional topology such as combinatorial study of three-dimensional manifolds, knotted surfaces in four-dimensional manifolds, and quantum invariants of knots and three-manifolds.The academic year 2002 : We publicized our results obtained in the academic year 2001. We also exchanged ideas with researchers and thus could make our new goals.In April the head investigator and Jun Murakami were invited to a workshop on the volume conjecture held at the University of Quebec at Montreal, Canada and gave talks. The volume conjecture was proposed by Jun Murakami and the head investigator generalizing R. Kashaev's conjecture. It would relate the colored Jones polynomials of knots to the geometric structures of the knot complements, and attracts many researchers all over the world. Kobayashi visited Korea Advanced Institute for Science and Technology in July and gave a series of lectures on three-dimensional manifolds. Taniyama gave an invited lecture on links in graphs at the international conference 'Geometric Topology' held at Xian, China. Ohtsuki published a book 'Quantum invariants ・・A study of knots, 3-manifolds, and their sets', which describes quantum invariants including his own results.

2001学年：我们在京都大学数学科学研究所组织了为期一年的研究项目“世纪的低维拓扑”在这个项目中，我们邀请了来自日本国内外的低维拓扑学家。我们有大约50名来自海外的访客，我们可以交换信息，并可以通过许多讲座讨论各个领域。因此，我们可以在低维拓扑的许多领域获得新的方面，如三维流形的组合研究，四维流形中的纽结曲面，纽结和三维流形的量子不变量。2002学年：我们公布了我们在2001学年获得的结果。我们还与研究人员交换了意见，从而可以使我们的新目标。4月，首席研究员和村上润应邀参加了在加拿大蒙特利尔的魁北克大学举行的关于体积猜想的研讨会，并发表了演讲。体积猜想是由Jun Murakami和主要研究者推广R. Kashaev猜想它将纽结的色琼斯多项式与纽结补的几何结构联系起来，吸引了国内外许多学者的研究。小林于7月访问了韩国科学技术高等研究院，并就三维流形进行了一系列讲座。谷山应邀演讲链接图在国际会议'几何拓扑'在西安举行，中国。Ohtsuki出版了一本书“量子不变量··研究结，3-流形，及其集”，其中描述了量子不变量，包括他自己的结果。

项目成果

Y.Ohyama, K.Taniyama, S.Yamada: "Realization of Vassiliev invariants by unknotting number one knots"Tokyo J.Math.. 25. 17-31 (2002)

Y.Ohyama、K.Taniyama、S.Yamada：“通过解开第一结来实现 Vassiliev 不变量”Tokyo J.Math.. 25. 17-31 (2002)

H.Murakami, T.Ohtsuki: "Finite type invariants of knots via their Seifert matrices"Asian Journal of Mathematics. 5・2. 239-386 (2001)

H.Murakami，T.Ohtsuki：“通过 Seifert 矩阵的结的有限类型不变量”亚洲数学杂志 5・2（2001）。

T.Ohtsuki: "Quantum invariants, -A study of knots, 3-manifolds, and their sets"World Scientific Publishing Co., inc.. 489 (2002)

T.Ohtsuki：“量子不变量，-结、3-流形及其集合的研究”世界科学出版有限公司，489 (2002)

H. Murakami and J. Murakami: "The colored Jones polynomials and the simplicial volume of a knot"Acta Math.. 186. 85-104 (2001)

H. Murakami 和 J. Murakami：“彩色琼斯多项式和结的单纯体积”Acta Math.. 186. 85-104 (2001)

H.Murakami, J.Murakami: "The colored Jones polynomials and the simplicial volume of a knot"Acta Mathematica. 186・1. 85-104 (2001)

H.Murakami，J.Murakami：“有色琼斯多项式和结的单纯体积”Acta Mathematica 186・1（2001）。