Künneth formulas for Cotor

IF 0.5 3区 数学 Q3 MATHEMATICS
A. Salch
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引用次数: 0

Abstract

We investigate the question of how to compute the cotensor product, and more generally the derived cotensor (i.e. Cotor) groups, of a tensor product of comodules. In particular, we determine the conditions under which there is a Künneth formula for Cotor. We show that there is a simple Künneth theorem for Cotor groups if and only if an appropriate coefficient comodule has trivial coaction. This result is an application of a spectral sequence we construct for computing Cotor of a tensor product of comodules. Finally, for certain families of nontrivial comodules which are especially topologically natural, we work out necessary and sufficient conditions for the existence of a Künneth formula for the 0th Cotor group, i.e. the cotensor product. We give topological applications in the form of consequences for the E2-term of the Adams spectral sequence of a smash product of spectra, and the Hurewicz image of a smash product of spectra.

科托尔的库奈特公式
我们研究的问题是如何计算张量的张量积,以及更广义地说,如何计算逗点的张量积的派生张量(即 Cotor)群。特别是,我们确定了存在 Cotor 的库奈特公式的条件。我们证明,当且仅当一个适当的系数逗点具有微不足道的协作用时,Cotor 群才有一个简单的库奈特定理。这一结果是我们为计算张量组合积的 Cotor 而构建的谱序列的应用。最后,对于某些在拓扑学上特别自然的非琐碎协元族,我们为第 0 次 Cotor 群(即张量积)的库奈特公式的存在提出了必要条件和充分条件。我们给出了拓扑应用,即谱的粉碎积的亚当斯谱序列的 E2 项和谱的粉碎积的胡勒维茨像的后果。
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来源期刊
CiteScore
1.50
自引率
12.50%
发文量
226
审稿时长
4-8 weeks
期刊介绍: The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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