New Developments ofAlgebtaic Topology

代数拓扑学的新进展

基本信息

批准号：
16340015
负责人：
MINAMI Norihiko
金额：
$ 9.7万
依托单位：
Nagoya Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340015/
关键词：
Stable Homotopy choromatic tower Obstruction Theory Equivariant Homotopy Theory Seiberg-Witten Invariants Quasi Category Homotonical Algebraic Geometry Motif Theory 特性類 4次元多様体 Spanier-Whitehead圏 Fredholm Universe

项目摘要

Following some strong demand of the investigator Tsuchiya, the head investigator, Minami embarked upon intensive rematch on the dg-category theory of Keller, Toen, Tabuada, and on the derived algebraic geometry of Toen-Vezzosi and Lurie. Although prominent results are yet to be discovered in these disciplines, some dividends have been obtained to study the Hopkins Chromatic Splitting Conjecture, one of the most fundamental problems in the stable homotopy theory. Also, concerning the fundamental Tate conjecture in the motif theory of algebraic geometry, the head investigator Minami pointed out a fatal mistake in someone's acclaimed solution of the Tate conjecture, and realized a possibly new promising approach to the Tate conjecture.The investigator Tsuchiya made a big progress in the conformal field theory on the Riemman surface associated with the vertex operator algebra satisfying the C2 condition. The investigators Furuta and Kametani obtained a perhaps, under the current level of algebraic topology, the decisive result on the Bauer-Furuta-Seiberg-Witten invariants when hi is positive. The invesitagator Shimakawa opened up a completely new approach to the compact Lie group equivariant generalized cohomology theories, from the view point of the labeled configuration spaces and continuous functors.Very recently, the investigator Kobayashi, making full use of Perelman's method, has obtained a series of prominent results, including an affirmative andwer to Lebrun's conjecture. This is a very important achievement which is well beyong the head investigator's initial expectations.

根据研究人员Tsuchiya的一些强烈要求，Minami的首席研究员开始对Keller，Toen，Toen，Tabuada和Toen-Vezzosi和Lurie的派生代数几何形状进行密集的重赛。尽管在这些学科中尚未发现突出的结果，但已经获得了一些股息来研究霍普金斯色素分裂猜想，这是稳定同型理论中最根本的问题之一。 Also, concerning the fundamental Tate conjecture in the motif theory of algebraic geometry, the head investigator Minami pointed out a fatal mistake in someone's acclaimed solution of the Tate conjecture, and realized a possibly new promising approach to the Tate conjecture.The investigator Tsuchiya made a big progress in the conformal field theory on the Riemman surface associated with the vertex operator algebra satisfying the C2条件。研究人员Furuta和Kametani在当前代数拓扑的水平上获得了可能的果断结果，当HI为正时，Bauer-Furuta-Furuta-Furuta-Furuta-seiberg-witten不变性。从标记的配置空间和连续的函数的角度来看，入侵者Shimakawa为紧凑的谎言集团普遍的共同体理论打开了一种全新的方法。这是一个非常重要的成就，这很好地是首席调查员的最初期望。

项目成果

期刊论文数量（113）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Phantoms which emerge between Spanier-Whitehead and the stable homotopy.

斯潘尼尔-怀特海和稳定同伦之间出现的幻象。

DOI：
发表时间：
2006
期刊：
影响因子：
0
作者：
Norihiko;Minami
通讯作者：
Minami

Derived Algebraic Geometry and Elliptic Cohomology,followingLurie and Toen-Vezzosi

遵循 Lurie 和 Toen-Vezzosi 的推导代数几何和椭圆上同调

DOI：
发表时间：
2008
期刊：
影响因子：
0
作者：
Mikio Furuta;Yukio Kametani;Hirofumi Matsue;Norihiko Minami;Norihiko Minami;Norihiko Minami;Norihiko Minami;Norihiko Minami;南範彦;南範彦
通讯作者：
南範彦

Derived Artin's Representability Criterion

派生 Artin 的代表性准则