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Study of Discrete Subgroups of Rank 1 Simple Groups by Geometric Methods

一阶单群离散子群的几何方法研究

基本信息

批准号：
13440019
负责人：
NAYATANI Shin
金额：
$ 7.55万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440019/
关键词：
fixed point theorem quaternionic CR structure minimal surface lemma of logarithmic derivative SL(2,C) representation space crystal lattice symplectic filling deformation space of q.Fuchsian group 四元数CR幾何双曲多様体磁場付き推移作用素 A_∞代数フレアーコ

项目摘要

Shin Nayatani and Hiroyasu Izeki studied combinatorial harmonic map theory and its application to super-rigidity and fixed point theorem, and proved fixed point theorems for isometric actions of discrete groups on CAT(O) spaces. Shin Nayatani and HIroyuku Kamada studied quaternionic CR geometry, and clarified the representation-theoretic meaning of the canonical pseudohermitian connection.Norio Ejiri studied the existence problem for non-area-minimizing stable minimal surface of genus g in 2g-dimensional flat tori, and proved that there exists a non-holomorphic stable minimal surface of genus【greater than or equal】4 in a certain 8-dimensional torus.Ryoichi Kobayashi srudied the construction of geometric theory of Diophantine approximation as discretization of the Nevanlinna theory, and showed that the lemma of logarithmic derivative for holomorphic curves in protective algebraic varieties hold always with the same form.Toshihiro Nakanishi introduced a parameter complexifying R.C.Penner … More 's λ length on the spaces of equivalence classes of faithful representations from surface groups into SL(2,C) mapping homotopy classes of boundary components to parabolic elements. Using this he succeeded in representing the mapping class groups as groups of rational transformations.Motoko Kotani studied the large deviation of the random walk on a crystal lattice, that is, an infinite graph on which an abelian group acts and its geometric meaning. She determined asymptotic terms and clarified the relation between the rate function representing decay order and the tangent cone at infinity of a crystal lattice.Hiroshi Ohta completely determined the deformation classes of symplectic fillings of the links of simple singularities and simple elliptic singularities. He also studied the obstruction and deformation theories of the Floer cohomology using filtered A_∞ algebras.Takeshi Sato obtained some new algorithms to compute the value of π using various modular functions.Hiroyuki Kamada studied compact complex surfaces admitting scalar flat Kahler metrics, and characterized the product of complex projective lines in terms of the existence of such metrics with a certain type of symmetry.Kentaro Ito studied the boundary behavior of the deformation space of quasi-Fuchsian groups by means of the holonomy representations of projective structures on surfaces. He proved that Goldman's grafting theorem holds for the boundary groups by showing a certain kind of continuity and discreteness, thus resolving Bromberg's conjecture. Less

Shin Nayatani和Hiroyasu Izeki研究了组合调和映射理论及其在超刚性和不动点定理中的应用，证明了CAT(O)空间上离散群的等距作用的不动点定理。Shin Nayatani和Hiroyuku Kamada研究了四元数CR几何，阐明了正则伪Hermite联络的表示理论意义。Norio Ejiri研究了2g维平环面中亏格g的非面积最小化稳定极小曲面的存在性问题，证明了在某一8维环面上存在亏格[大于或等于]4的非全纯稳定极小曲面。小林龙一研究了丢番图逼近几何理论的构造，作为对nevanlinna理论的离散化并证明了保护代数簇中全纯曲线的对数导数引理始终保持相同的形式。Toshihiro Nakanishi引入了一个使R.C.Penner…复杂化的参数S在曲面群到SL(2，C)的忠实表示等价类空间上的λ长度。利用这一点，他成功地将映射类群表示为有理变换群。小谷元子研究了晶格上随机游动的大偏差，即阿贝尔群作用于其上的无限图及其几何意义。她确定了渐近项，并阐明了表示衰变级数的速率函数与晶格无穷远处的切锥之间的关系。太田宏志完全确定了简单奇点和简单椭圆奇点链环的辛填充项的变形类。他还利用滤子A_∞代数研究了Floer上同调的阻塞和形变理论。佐藤武利用各种模函数得到了一些计算π值的新算法。Kamada Hiroyuki研究了具有标量平坦Kahler度量的紧复曲面，并利用这种度量的存在性刻画了复射影线的乘积。伊藤健太郎利用曲面上射影结构的完整表示研究了拟富氏群变形空间的边界行为。他通过证明某种连续性和离散性，证明了戈德曼的嫁接定理对边界群成立，从而解决了Bromberg猜想。较少