Invariants of knots and 3-manifolds

结和 3 流形的不变量

基本信息

批准号：
15540063
负责人：
OHTSUKI Tomotada
金额：
$ 1.09万
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：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540063/
关键词：
Knot 3-manifold Invariant Kontsevich invariant 2-loop polynomial 2ループ多項式

项目摘要

I organized researches on invariants of knots and 3-manifolds.I edited the proceedings of the workshop "Invariants of Knots and 3-Manifolds", which I organized in September 2001, and published the proceedings from the journal Geometry and Topology Monographs. In particular, I edited a list of problems, which was made based on problems given in the problem sessions of the workshop, and published it as a part of the proceedings.I studied the loop expansion of the Kontsevich invariant, in particular, the 2-loop polynomial, which presents the 2-loop part of the loop expansion. I presented the 2-loop polynomial of a knot in terms of finite type invariants 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 knot complement. I obtained a bound of the degree of the 2-loop polynomial of a knot by twice the genus of the knot, by calculating the presentation concretely … More introducing Gaussian diagrams. Further, I gave explicit presentations of the 2-loop polynomial for the torus knots and the knots of genus 1. Furthermore, I showed a cabling formula for the 2-loop polynomial, which gives the 2-loop polynomial for any cable knot of a given knot.I organized a low-dimensional topology seminar, jointly with Kazuo Habiro, who is a co-investigator of this research. The speakers were Sergei Duzhin, Kazuhiro Hikami, Andrew Kricker, Julien Marche, Jean-Baptiste Meilhan, Gregor Masbaum, Jorgen Andersen, Yoshiyuki Yokota, Jozef Przytycki, and their talks were on advanced topics in the area of invariants of knots and 3-manifolds. In particular, by financial supports from the grant of this research, Kricker and Marche stayed at the RIMS in two weeks. I think their talks and stays 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. Less

我组织了我在2001年9月组织的研讨会“结和3个manifolds”研讨会的会议记录的研究，并从《几何学和拓扑专着》中发表了会议记录。特别是，我编辑了一系列问题列表，这些问题是根据研讨会的问题会议中给出的问题的，并将其作为程序的一部分发布。我以结的有限型脊柱的有限型不变性来介绍结的2环多项式，从我认为结的2环多项式视为结的无限循环盖。我通过结实地计算出呈递的表现，从而获得了结的两倍的结属。此外，我给出了2环的多项式的明确介绍。研究。演讲者是Sergei Duzhin，Kazuhiro Hikami，Andrew Kricker，Julien Marche，Jean-Baptiste Meilhan，Gregor Masbaum，Jorgen Andersen，Jorgen Andersen，Yoshiyuki Yokota，Jozef Przytycki，他们的对话以及他们在Invariant of Invariant of Invarianf of Invarianf of Invarys of Invarianf and of Invarys的对话。特别是，通过这项研究的授予，克里克（Kricker）和马尔凯（Marche）在两周内留在了轮辋。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，他们与研究生（例如研究生）之间的研究互动的角度来看，他们的演讲和住宿非常好。较少的

项目成果

期刊论文数量（16）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

結び目と3次元多様体の不変量

结和 3 流形的不变量

DOI：
发表时间：
2003
期刊：
数学(日本数学会編集)(岩波書店) 55
影响因子：
0
作者：
K.Mikami;T.Mizutani;大槻知忠
通讯作者：
大槻知忠

A cabling formula for the 2-loop polynomial of knots

结的 2 环多项式的布线公式

DOI：
发表时间：
2004
期刊：
Publ.RIMS, Kyoto Univ. 40
影响因子：
0
作者：
M.Brittenham;C.Hayashi;M.Hirasawa;T.Kobayashi;K.Shimokawa;K.Sakai (with K.H.Lee);H.konno;M.Miyanishi;T.Ohtsuki
通讯作者：
T.Ohtsuki

Invariants of knots and 3-manifolds

结和 3 流形的不变量