权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

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

我组织了关于纽结和3-流形的不变量的研究。我编辑了2001年9月组织的“纽结和3-流形的不变量”研讨会的会议记录，并在《几何和拓扑学专著》杂志上发表了会议记录。特别是，我编辑了一个问题列表，这是根据在讲习班的问题会议上给出的问题，并将其作为会议录的一部分发表。我研究了Kontsevich不变量的循环扩展，特别是2-loop多项式，它表示循环扩展的2-loop部分。我根据纽结的塞弗特曲面的脊的有限型不变量来给出纽结的2-循环多项式，从我将纽结的2-循环多项式视为纽结补的无限循环覆盖的等变卡森不变量的角度出发。通过具体的计算，得到了纽结的2-圈多项式的次数以纽结亏格的2倍为界的一个界 ...更多信息介绍高斯图。此外，我给出了明确介绍的2-循环多项式的环面结和结的亏格1。此外，我还展示了2-loop多项式的布线公式，它给出了给定结的任何电缆结的2-loop多项式。我与本研究的合作研究者Kazuo Habiro共同组织了一个低维拓扑研讨会。发言者谢尔盖Duzhin，Kazuhiro Hikami，安德鲁Kricker，朱利安马尔凯，让巴蒂斯特梅尔汉，格雷戈尔Masbaum，约根安徒生，Yoshiyuki横田，约瑟夫Przytycki，他们的会谈是先进的主题领域的不变量的结和3流形。特别是，通过这项研究的资助，Kricker和马尔凯在RIMS呆了两周。我认为，从他们与我和共同研究者之间的共同研究的角度来看，以及从他们与研究生等年轻研究人员之间的研究互动的角度来看，他们的谈话和停留都非常好。少

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