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2次元結び目とYang-Millsゲージ理論について

关于二维结和 Yang-Mills 规范理论

基本信息

批准号：
20K22319
负责人：
谷口正樹
金额：
$ 1.83万
依托单位：
Institute of Physical and Chemical Research
依托单位国家：
日本
项目类别：
Grant-in-Aid for Research Activity Start-up
财政年份：
2020
资助国家：
日本
起止时间：
2020-09-11 至 2024-03-31
项目状态：
已结题

项目摘要

本研究の研究目標は, 2次元結び目をYang-Millsゲージ理論を用いて研究することであった. 本研究課題の主結果であった論文「Seifert hypersurfaces of 2-knots and Chern-Simons functional」においてYang-Millsゲージ理論を用いて2次元結び目のSeifert超曲面と結び目補空間のSU(2)表現を結びつけるに至っていた. また, 前年度は, その議論を2次元トーラスがS^1×S^3にessentialに埋め込まれている場合に拡張できることを考察していた. また, 関連する議論として, 2次元トーラスとS^1×S^3のペアとしての無限巡回被覆空間を考察し, その上のYang-Millsインスタントンモジュライ空間のコンパクト性を考察し, 上記に述べた一部の結果はそのようなモジュライ空間から導かれることを考察した. また, Daemi-佐藤-Scaduto-井森-谷口の研究において特異インスタントン理論を用いて結び目の実数値不変量J(K)を導入し, そこからあるクラスの2次元トーラス結び目に対しても実数値不変量が拡張できることを考察した.これは, 2次元トーラス結び目のスライスが結び目Kである場合に, J(K)は, 2次元トーラス結び目になる, という考察を経て得られる. すなわち, スライスとなる結び目の取り方に依存しないことが分かる. このようにして2次元トーラス結び目の実数値不変量が新しく得られた.

The purpose of this study is to use the second-order results to study the theory of Yang-Mills theory. The main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study are as follows: in this study, the main results of this study In the previous year, we will discuss the two-dimensional investigation of S ^ 1 × S ^ 3 essential. In this paper, we discuss the performance of the two-dimensional simulation system S ^ 1 × S ^ 3 for the unlimited roving of covered space, and then use the Yang-Mills system to verify the performance of the space vehicle. The last chapter describes the results of the review. Daemi- Sato-Scaduto- well-Mori-Taniguchi Research Institute. The theory of the study is based on the measurement of J (K) data. The results show that there are two steps in the study. The results of the two-dimensional survey show that the results of the two-dimensional survey show that the results of the two-dimensional test show that the results of the two-dimensional test show that the results of the survey show that the results are satisfactory. This is not true. The results show that the party is dependent on the number of points. Do not change the number of two-dimensional data. The results show that there are many new data available.

项目成果

期刊论文数量（32）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Intantons, special cycles, and knot concordance I

整数、特殊循环和结索引 I

DOI：
发表时间：
2022
期刊：
影响因子：
0
作者：
谷口正樹
通讯作者：
谷口正樹

Instanton Floer theory and local equivalence II

Instanton Florer 理论和局部等价 II

DOI：
发表时间：
2020
期刊：
影响因子：
0
作者：
Kosuke Mitarai ; Yasunari Suzuki ; Wataru Mizukami ; Yuya O. Nakagawa ; Keisuke Fujii;Masaki Taniguchi
通讯作者：
Masaki Taniguchi

Construction of equivariant singular knot Floer homology I

等变奇异结Floer同调I的构建