Topology related to invariants of knots and 3-manifolds

与结和 3 流形不变量相关的拓扑

基本信息

批准号：
13640064
负责人：
OHTSUKI Tomotada
金额：
$ 2.56万
依托单位：
The University of Tokyo (2002)Tokyo Institute of Technology (2001)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
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/grant/KAKENHI-PROJECT-13640064/
关键词：
knot 3-manifold invariant

项目摘要

By the support of the grant-in-aid I organized the workshop and seminars "Invariants of Knots and 3-Manifolds" at the Research Institute for Mathematical Sciences (RIMS), Kyoto University in September 2001, as activities of the 2001 RIMS research project "Low-Dimensional Topology in the Twenty-First Century". We had 70 domestic participants and 26 foreign participants.Historically speaking, this research area is a relatively new area based on the enormous number of invariants, called quantum invariants, of knots and 3-manifolds, which have been derived from the Chern-Simons field theory in the 1980s. I think the topological reconstruction of these invariants has almost been completed by various works of these decades.An aim of the workshop and seminars was to discuss future directions for this area.To discuss these matters fully, I planned 1 month of activities, relatively longer than usual.Further, to encourage discussions among the participants, we arranged a short problem session after each talk, and requested the speaker to give his/her open problems there.Many interesting problems were presented in these problem sessions and, based on them, we had valuable discussions in and between seminars and the workshop.I edited open problems discussed there into a problem list, which, I hope, will clarify the present frontier of this area and assist readers when considering future directions.The proceedings of the workshop was published in the online journal "Geometry and Topology Monographs".The problem list will also be published as a part of the proceedings.

在赠款中，我在2001年9月在京都大学的数学科学研究所（RIMS）组织了研讨会和研讨会“结和3个模型”，作为2001年RIMS研究项目的活动“京都大学的活动”。我们有70名国内参与者和26名外国参与者。从历史上讲，该研究领域是一个相对较新的领域，基于众多不变的量子，称为量子不变的人，是结和3个manifolds，它们是从1980年代的Chern-Simons Field Theory衍生而来的。我认为这些不变的拓扑重构几乎已经由这些数十年的各种作品完成。研讨会和研讨会的目的是讨论该领域的未来指示。要充分讨论这些问题，我计划了一个月的活动，相对较长，比平时更长。further，further，鼓励参与者之间的讨论，我们在介绍的问题上介绍了一个问题。这些问题会议以及基于这些会话，我们在研讨会和研讨会之间进行了有价值的讨论。我在此处讨论了一个问题列表，我希望该问题会澄清该领域的当前边界，并在考虑未来的方向时协助读者。在在线杂志上发表了“少年和拓扑列表”。