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

Homotopy theoretical research of manifolds

流形的同伦理论研究

基本信息

批准号：
11640069
负责人：
ISHIMOTO Hiroyasu
金额：
$ 1.28万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640069/
关键词：
primary manifolds homotopy equivalent manifolds constant mean curvature surfaces harmonic inverse mean curvature surfaces hypersurface isolated singularities Milnor number Pn'mes and Knots automorphic forms 多様体のホモトピー同値ボンネ曲面ブローイングアップ

项目摘要

(1) Ishimoto studied the problem whether the matter corresponding to the Poincare conjecture holds or not for primary manifolds which are m-spheres with attached q-handles in the metastable range. For that purpose, he intended to extend the James-Whitehead theorem to the one for primary manifolds and succeeded in such case that the quadratic forms which distinguish primary manifolds take values in a cyclic group. Using the result, he proved in almost all cases that the matter in question also valid when the cyclic group is Z_<24>, adding to the results already obtained.(2) Fujioka studied the fundamental properties of harmonic inverse mean curvature surfaces which are natural generalization of constant mean curvature surfaces. In particular, he characterized such a surface as the one which admits a transformation preserving a certain quantity represented with curvature. He studied also the Bonnet surfaces.(3) Tomari studied the theory of multiplicity of filtered rings, and as an application, he constructed a criterion formula for the Milnor number of f which gives the definition of hyper surface isolated singularities, using the weight of coordinates and the Taylor expansion.(4) Morishita studied analogies between knots and primes, 3-manifolds and number fields, basing on the analogy between link groups and Galois groups, and tried to bridge between the algebraic number theory and the 3-dimensional topology. He also studied with K, Murasugi in Toronto.(5) Sugano studied the automorphic forms on unitary groups of degree 3 in number theory. He gave the explicit expansion for Eisenstein series and Kudla lift images using primitive theta functions, and gave the non-vanishing condition for the Kudla lift in terms of the periods.

(1)Ishimoto研究的问题是否对应于庞加莱猜想成立或不适用于准流形的m-球附加q-处理的亚稳范围。为此，他打算将詹姆斯-怀特黑德定理推广到初等流形，并在区分初等流形的二次型在循环群中取值的情况下取得了成功。使用的结果，他证明了在几乎所有情况下，问题也有效时，循环群是Z_<24>，增加到已经获得的结果。(2)Fujioka研究了调和逆平均曲率曲面的基本性质，调和逆平均曲率曲面是常平均曲率曲面的自然推广。特别是，他的特点是这样一个表面作为一个承认变换保持一定数量表示曲率。他还研究了阀盖表面。(3)托马里研究了理论的多重性过滤环，并作为一个应用，他建造了一个准则公式的米尔诺数的f给出了定义超表面孤立奇点，使用的重量坐标和泰勒展开。(4)森下研究类比之间的结和素数，3-流形和数域，基于类比之间的联系群和伽罗瓦群，并试图弥合代数数论和三维拓扑。他还曾在多伦多与K，Murasugi学习。(5)Sugano在数论中研究了3次酉群的自守形式。他给出了显式扩展的爱森斯坦系列和库德拉电梯图像使用原始theta函数，并给出了非零条件库德拉电梯方面的时期。