Analysis of the differential (co)torsion products with algebraic models for spaces
用空间代数模型分析微分(共)扭转积
基本信息
- 批准号:14540095
- 负责人:
- 金额:$ 1.22万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2002
- 资助国家:日本
- 起止时间:2002 至 2004
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The bar and cobar type Eilenberg-Moore spectral sequences (EMSS) are of great use in studying cohomology algebras of many interesting spaces, for example, the classifying spaces, a pull-back on spaces and function spaces. In the construction of the spectral sequences, the differential (co)torsion product functors play an important role. The purpose of this research is to analyze such product functors from the viewpoint of the algebraic models for spaces. Moreover, we attempt to relate algebraic properties, which is deduced from the consideration of resolutions computing the (co)torsion functors, with topological properties of spaces.The results are as follows. In [2], we have given a model for the EMSS by applying the shc-minimal model for spaces. A collapse theorem for the spectral sequence is also proved. In [3], we have constructed the cobar type EMSS converging to the cohomology of the space of invariant paths. Let M be a simply connected Riemannian manifold. By combining the fact … More obtained by analyzing the EMSS with the result concerning invariant geodesics due to Tanaka, we have proved that every isometry on M has infinite many invariant geodesics if, as an algebra, H^*(M ; Z/2)〓H^*(S^p×S^q ; Z/2) with p≠q. The head investigator has introduced a notion of the module derivation with values in a torsion product. In [4], by using the derivation, we have given a sufficient condition for the evaluation fibration not to be totally non cohomologous to zero with respect to a given field. One of the theorems in [5] asserts that the isomorphism class of an SU(n)-adjoint bundle over 4-dimensional complex X coincides with the homotopy equivalence class of the bundle. The technical device for proving that is the module derivation with values in the Hochschild homology of H^*(X ; Z/p). Let S be a non-orientable surface and BG the classifying space of a simply connected Lie groups whose homology is p-torsion free. In [6], by calculating the EMSS which arises from a pull-back associated with a cofibre square, the cohomology algebra H^* (Map(S, BG) ; Z/p) is determined explicitly. Here Map(S, BG) denotes the function space of all maps from S to BG. The two approaches to the cohomology of spaces, namely, the use of algebraic models and the consideration of resolutions computing (co)torsion products, are unified via the work in [1] on the cohomology of the classifying space of loop groups. In consequence, with the aid of the computation of twisted tensor products, the cohomology H^* (BLSpin(10) ; Z/2) is determined as a module. Less
Bar型和Cobar型Eilenberg-Moore谱序列(EMSS)在研究许多有趣空间的上同调代数中有着重要的应用,如分类空间、拉回空间和函数空间等。在谱序列的构造中,微分(余)挠积函子起着重要的作用。本研究的目的是从空间代数模型的角度分析此类积函子。此外,我们还试图将由计算(余)挠函子的分解所导出的代数性质与空间的拓扑性质联系起来,得到如下结果.在[2]中,我们应用空间的shc-极小模型给出了EMSS的一个模型。证明了谱序列的一个塌缩定理。在[3]中,我们构造了收敛于不变路空间上同调的cobar型EMSS。设M是单连通黎曼流形。通过结合事实 ...更多信息 本文利用Tanaka关于不变测地线的结果分析EMSS,证明了M上的每一等距线都有无穷多个不变测地线,如果作为代数,H^*(M ; Z/2)<$H^*(S^p×S^q ; Z/2),其中p <$q.首席研究员介绍了一个概念的模块导函数的值在扭转产品。在[4]中,通过推导,我们给出了评价纤维化相对于给定域不完全非余同调于零的充分条件。文[5]中的一个定理断言4维复X上的SU(n)-伴随丛的同构类与丛的同伦等价类一致。证明这一点的技术手段是模导子,其值在H^*(X ; Z/p)的Hochschild同调中。设S是不可定向曲面,BG是同调无p-挠的单连通李群的分类空间。在[6]中,通过计算由与上纤维平方相关的拉回引起的EMSS,明确确定了上同调代数H^*(Map(S,BG); Z/p)。这里Map(S,BG)表示从S到BG的所有映射的函数空间。研究空间上同调的两种方法,即利用代数模型和考虑分解计算(余)挠积,通过文[1]关于环群分类空间的上同调的工作得到了统一。因此,借助于扭曲张量积的计算,上同调H^*(BLSpin(10); Z/2)被确定为一个模。少
项目成果
期刊论文数量(13)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Module derivations and non triviality of an evaluation fibration
评估纤维的模块推导和非平凡性
- DOI:
- 发表时间:2002
- 期刊:
- 影响因子:0
- 作者:A.Kono;K.Kuribayashi;K.Kuribayashi
- 通讯作者:K.Kuribayashi
Katsuhiko Kuribayashi: "Module derivations and non triviality of an evaluation fibration"Homology, Homotopy and Applications. 4. 87-101 (2002)
Katsuhiko Kuribayashi:“模块推导和评估纤维的非平凡性”同源性、同伦性和应用。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Twisted tensor products related to the cohomology of the classifying spaces of loop groups
与环群分类空间上同调相关的扭曲张量积
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:K.Kuribayashi;M.Mimura;T.Nishimoto
- 通讯作者:T.Nishimoto
Katsuhiko Kuribayashi: "The cohomology of a pull-back on K-formal spaces"Topology and Its Appllications. 125. 125-159 (2002)
Katsuhiko Kuribayashi:“K-形式空间上的回拉的上同调”拓扑及其应用。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Module derivations and cohomological splitting of adjoint bundles
伴随丛的模导数和上同调分裂
- DOI:
- 发表时间:2003
- 期刊:
- 影响因子:0
- 作者:A.Kono;K.Kuribayashi
- 通讯作者:K.Kuribayashi
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KURIBAYASHI Katsuhiko其他文献
KURIBAYASHI Katsuhiko的其他文献
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{{ truncateString('KURIBAYASHI Katsuhiko', 18)}}的其他基金
Studies on stratifolds by a categorical approach
通过分类方法研究分层
- 批准号:
16K13753 - 财政年份:2016
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Studies on association schemoids with insights gained from cohomology theory of small categories
基于小范畴上同调理论的关联模式研究
- 批准号:
25610002 - 财政年份:2013
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Studies on rational visibility problems of a Lie Group and extensions of symplectic classes by a model for the evaluation map
用评价图模型研究李群有理可见性问题和辛类的扩展
- 批准号:
20540070 - 财政年份:2008
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for Scientific Research (C)