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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.

在该基金的支持下，我于2001年9月在京都大学数学科学研究所（RIMS）组织了“结和3流形的不变量”讲习班和研讨会，作为2001年RIMS研究项目“二十一世纪的低维拓扑”的活动。我们有 70 名国内参与者和 26 名外国参与者。从历史上看，这个研究领域是一个相对较新的领域，基于大量的结和 3 流形不变量，称为量子不变量，这些不变量源自 20 世纪 80 年代的 Chern-Simons 场论。我认为这些不变量的拓扑重构已经通过这几十年来的各种工作几乎完成了。研讨会和研讨会的目的是讨论这个领域的未来方向。为了充分讨论这些问题，我计划了1个月的活动，比平时相对更长。此外，为了鼓励参与者之间的讨论，我们在每次演讲后安排了一个简短的问题会议，并要求演讲者在那里提出他/她的开放性问题。许多有趣的问题在这些问题会议，并在此基础上，我们在研讨会和研讨会之间进行了有价值的讨论。我将其中讨论的开放性问题编辑成问题列表，我希望这将澄清该领域目前的前沿，并在考虑未来方向时帮助读者。研讨会的会议记录发表在在线期刊“几何和拓扑专着”上。问题列表也将作为会议记录的一部分出版。