Studies on the Cohomology of Mapping Class Groups, Coxeter Groups and Artin Groups

映射类群、Coxeter群和Artin群的上同调研究

基本信息

批准号：
17540056
负责人：
AKITA Toshiyuki
金额：
$ 2.24万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

The cohomology of discrete groups, such as mapping class groups of closed surfaces, Coxeter groups and Artin groups, is one of the important objects in topology as well as geometry In this research project, we studied the cohomology of discrete groups. The following three subjects were emphasized in the project:(1) Relations with the cohomology of finite subgroups(2) Actions of discrete groups on manifolds/complexes and combinatorial structures(3) Algebraic methods (such as combinatorics and free resolutions)Concerning of (1), Akita and Kawazumi proved integral Riemann-Roch formulae for cyclic subgroups of mapping class groups, which are variants of Grothedieck-Riemann-Roch theorem for integral cohomology. Concerning of (2), Izeki and Hosaka obtained various results concerning of group actions and geometric structures Finally, concering of (3), Akita proved alternative formulae for the Euler characteristics of even dimensional triangulated manifolds. The key ingredient to prove the formulae is generalized Dehn-Sommerville equations obtained by Klee. In addition, Akita showed that mod p Riemann-Roch formulae hold for various cases, by using Kummer's congruences in classical number theory.

我们研究了该研究项目的拓扑组和几何学的重要对象之一，例如封闭表面，Coxeter组和ARTIN组的映射群体组之一，例如绘制封闭表面，Coxeter组和ARTIN组的共同体，我们研究了离散群体的共同体，我们研究了离散的组之一。 The following three subjects were emphasized in the project:(1) Relations with the cohomology of finite subgroups(2) Actions of discrete groups on manifolds/complexes and combinatorial structures(3) Algebraic methods (such as combinatorics and free resolutions)Concerning of (1), Akita and Kawazumi proved integral Riemann-Roch formulae for cyclic subgroups of mapping班级组，是Grothedieck-Riemann-Roch Roch综合共同体学定理的变体。关于（2），Izeki和Hosaka的群体作用和几何结构获得了各种结果，最终，关于（3）的（3），Akita证明了偶数三角歧管的Euler特征的替代公式。证明公式的关键要素是Klee获得的广义Dehn-Sommerville方程。此外，Akita表明，通过使用Kummer在经典数理论中的一致性，Mod P Riemann-Roch公式适用于各种情况。

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

On mod p Riemann-Roch formulae for mapping class groups

映射类群的 mod p Riemann-Roch 公式

DOI：
发表时间：
2008
期刊：
Advanced Studies in Pure Math 52
影响因子：
0
作者：
A.Ichino;T.Ikeda;A. Ichino;T. Ikeda;平賀郁;K. Hiraga;K. Hiraga;池田保;A. Ichino;市野篤史;市野篤史;T. Ikeda;平賀郁;T. Ikeda;平賀郁;市野篤史;T.Shoji;D.Nakano;T.Tanisaki;T.Shoji;D.Nakano;N.Enomoto;S.Ariki;T.Tanisaki;M.Kashiwara;T.Tanisaki;M.Kashiwara;T.Tanisaki;M.Kashiwara;H.Nakajima;S.Ariki;N.Sawada;S.Naito;T.Tanisaki;谷崎俊之;M.Kashiwara;大本亨;大本亨;T. Ohmoto;T. Ohmoto;T. Akita
通讯作者：
T. Akita

Strong reflection rigidity of Coxeter systems of dihedral groups

二面体群 Coxeter 系统的强反射刚度