The computation of the topological invariants of mapping spaces between Lie gorups

李群间映射空间拓扑不变量的计算

• 批准号: 05640134
• 负责人: KOZIMA Kazumoto
• 金额: $ 1.09万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05640134/
• 关键词: Lie group; Loop space; Loop group; Cohomology group; Function space; ホモロジー群

Let X be a connected fiber of a Lie group (or finite H-space) G.By evaluating of the adjoint map G*OMEGA^nX*OMEGA^nX on cohomology, one can get information of the cohomology of the space of type Map (S^n, G). We investigate this problem by using a computer aided symbolic computation and the theoritical computation based Hopf algebra structures and cohomology operations. We got some results by the computer aided computation and could get more general results by the theoritical method.Especialy, for the case G is the Dwyer-Wilkerson's H-space, Spin (n) and Sp (n) (and the connected fibers of these spaces), we could evaluate the adjoint maps on the cohomology. These result show that the homotopy type of the space like Map (S^n, G) is ristricted strongly by these adjoint map.We got also the result about the commutator map and its lift to the connected fiber space. As an application of this, we can prove the unknown result about the homotopy commutativity of the rotation group.The symbolic caliculation like effective homology causes a hevy intermidiate explosion of computation and it makes very hevy garbage collection on the symbolic computaion system. About this problem, S.Matsui applied the method of parallel and conditional garbage collection and reduced GC time.K.Kawahigashi investigated the application to phisical phenomina which some properties of the low dimensional Lie group affects.

设X是李群（或有限H-空间）G的连通纤维，通过对伴随映射G*OMEGA^nX*OMEGA^nX的上同调赋值，可以得到Map（S^n，G）型空间的上同调信息.我们利用计算机辅助符号计算和基于Hopf代数结构和上同调运算的理论计算来研究这个问题。特别地，当G是Dwyer-Wilkerson的H-空间，Spin（n）和Sp（n）（以及这些空间的连通纤维）时，我们可以计算伴随映射的上同调。这些结果表明，空间类映射（S^n，G）的同伦型受到这些伴随映射的强约束，并得到了交换子映射及其到连通纤维空间的提升的结果。作为其应用，我们可以证明旋转群同伦交换性的未知结果.有效同调等符号计算引起了计算量的巨大的中间爆炸，并在符号计算系统上造成了巨大的垃圾收集.针对这一问题，松井（S.Matsui）采用了并行的条件垃圾收集方法，减少了GC时间，川东（K.Kawahigashi）研究了低维李群的某些性质对物理现象的影响。

项目成果

A.Kono-K.kojima: "The adjoint action of the Dwyer-Wilkerson H-space on its loop space" J.Math.Kyoto Univ.35-1. 53-62 (1995)

A.Kono-K.kojima：“Dwyer-Wilkerson H 空间在其循环空间上的伴随作用”J.Math.Kyoto Univ.35-1。

M.Ichimura-K.Nishida K.Kawahigashi: "Spin-isospin response functions in quasi-elastic region" Nuchear Physics A. 577. 123-130 (1994)

M.Ichimura-K.Nishida K.Kawahigashi：“准弹性区域中的自旋-等位旋响应函数” Nuchear 物理 A. 577. 123-130 (1994)

Y.Tanaka-S.Matsui-A.Maeda-M.Nakanishi: "Partial Marking GC" Lecture Note in Computer Science (Springer). 854. 337-348 (1994)

Y.Tanaka-S.Matsui-A.Maeda-M.Nakanishi：计算机科学中的“部分标记 GC”讲义（Springer）。

T.N.Taddeucci, et al: "Momentum Dependence of the Nuclear Isovector Spin Responses from (p, n) Reactions at 494MeV" Physical Review Letters. 73. 3516-3519 (1994)

T.N.Taddeucci 等人：“494MeV (p, n) 反应的核等矢量自旋响应的动量依赖性”物理评论快报。

Y.Tanaka,S.Matsui,A.Maeda,M.Nakanishi: "Parallel Garbage Collection by Partial Marking and Conditionally Inuoked GC" Proceedings of the International Conference on Parallel Computing Technologies. 2. 397-408 (1993)

Y.Tanaka、S.Matsui、A.Maeda、M.Nakanishi：“通过部分标记和条件 Inuoked GC 实现的并行垃圾收集”并行计算技术国际会议论文集。