Topology of knots and 3-manifolds

结和 3 流形的拓扑

• 批准号: 11640065
• 负责人: OHTSUKI Tomotada
• 金额: $ 2.05万
• 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 (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640065/
• 关键词: Knot; 3-manifold; Quantum Invariant; Kontsevich Invariant; Vassiliev Invariant; Perturbative invariant; The LMO Invariant; Finite Type Invariant

The author had studied quantum and related invariants of knots and 3-manifolds, such as the Kontsevich invariant, Vassiliev invariants, perturbative invariants, the LMO invariant, and finite type invariants. In this research the author obtained various results on such invariants and their relations. Further, he completed a preliminary version of his book written as an extensive exposition on this topic.

作者研究了纽结和三维流形的量子不变量和相关的不变量，如Kontsevich不变量、Vassiliev不变量、微扰不变量、LMO不变量和有限型不变量。在这项研究中，作者得到了各种结果，这些不变量和它们之间的关系。此外，他完成了他的书的初步版本，作为对这一主题的广泛论述。

项目成果

T.Ohtsuki: "How to construct ideal points of SL2(C) representation space of knot groups"Topology Appl.. 93. 131-159 (1999)

T.Ohtsuki：“如何构造结群的 SL2(C) 表示空间的理想点”拓扑应用 93. 131-159 (1999)

大槻知忠、村上順、村上斉諸氏と共著: "量子不変量-三次元トポロジーと数理物理の遭遇"日本評論社. 154 (1999)

与大月智忠、村上淳、村上胜合着：《量子不变量——三维拓扑与数学物理的相遇》Nippon Hyoronsha 154 (1999)。

T.Ohtsuki: "The perturbativeSO(3) invariant of homology circles"Proceedings of the Conference on Low Dimensional Topology, Contemporary Math.. 233. 141-151 (1999)

T.Ohtsuki：“同调圆的微扰 SO(3) 不变量”低维拓扑会议论文集，当代数学.. 233. 141-151 (1999)

T.Ohtsuki & H.Murakami: "Finite type invariants of knots via their Seifert matrices"to appear in Asian J.Math..

大月T

Ohtsuki,Le,H.Murakami & J.Murakami : "A three-manifold invariant via the Kntsevich integral"Osaka J.Math.. 36-2. 365-396 (1999)

大月村上乐