Low-dimensional topology and algebraic structures

低维拓扑和代数结构

• 批准号: 22K03311
• 负责人: 葉廣 和夫
• 金额: $ 2.5万
• 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: 2022
• 资助国家: 日本
• 起止时间: 2022-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22K03311/
• 关键词: Yetter-Drinfeld加群; Hopf代数; タングル; 群コホモロジー; IA自己同型群; Hochschild-Serreスペクトル系列; 3次元多様体; 量子不変量; Kontsevich不変量

今年度は，以下の3本のプレプリントとして研究成果をまとめた。1. Ribbon Yetter-Drinfeld modules and tangle invariants(小鳥居祐香氏（広島大学）との共同研究）この論文ではモノイダル圏の中のピボタル対象、リボン対象の概念を定義した。この構成は、必ずしも双対を持たないモノイダル圏から、ピボタルあるいはリボンであるようなモノイダル圏を与える。この構成をHopf代数上のYetter-Drinfeld加群のbraided圏に適用することにより、Hopf代数上のribbon Yetter-Drinfeld加群の概念を得た。ribbon Yetter-Drinfeld加群を使ってタングルの不変量を構成することができることも示した。2. On the stable cohomology of the (IA-)automorphism groups of free groups(片田舞氏（京都大学D2）との共同研究）この論文では、群GL(n,Z)の代数的表現を係数とするコホモロジーに関するBorelの定理とHochschild-Serreスペクトル列を組み合わせることにより、ランクnの自由群F_nのIA自己同型群IA_nの安定域における有理コホモロジーについて考察した。特にこの安定コホモロジーの代数的な構造についての予想を提出し、Church-Farbによる表現安定性予想や片田氏のAlbaneseコホモロジーについての予想など、他の既知の予想との関連について考察した。3. On Borel's stable range of the twisted cohomology of GL(n,Z) (片田舞氏との共同研究）上記2.の論文に関連して、Borelの定理が成り立つための条件の改良について考察した。

This year, the following three books will be published in the following three books. 1. Ribbon Yetter-Drinfeld modules and tangle invariants (a joint study of Hsiao Hsiang-hsiang (University)). The concept of "elephant" is defined in this article. If you don't know what's going on, you have to make sure that you don't know what's going on, and you're going to have to make sure that you don't know what's going on. The concept of "Yetter-Drinfeld plus groups" on Hopf algebras and "ribbon Yetter-Drinfeld plus groups" on Hopf algebras is obtained by using the concept of ribbon Yetter-Drinfeld plus groups on ribbon Yetter-Drinfeld algebras. Ribbon Yetter-Drinfeld is added to the group to make sure that the quantity is changed to show that the data is not available. 2. On the stable cohomology of the (IA-) automorphism groups of free groups (jointly studied by Wushi Katada (Kyoto University D2), group GL (n) Z) it is shown that the number of algebras is similar to that of the Borel theorem. The Hochschild-Serre algebra lists the data of the free group, the free group, the homomorphic group, the IA_n, the stability domain, the rational stability domain, the stability domain, the rational stability, the stability domain, the rational stability, the stability domain, the stability In particular, the stability of the algebra is due to the fact that you want to propose it, and Church-Farb that you want to show your stability. You know, you know, you want to Albanese, you know, you want to know, you want to know, you know, you want to, you know, you know. 3. On Borel's stable range of the twisted cohomology of GL (nMagine Z) (joint study of Wushi Katada) Shangji 2. In this paper, the Borel theorem is established, the conditions are improved, and the conditions are investigated.

项目成果

ブルゴーニュ大学(フランス)

勃艮第大学（法国）