初等阿贝尔群的连通k理论的Tate上同调

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2019-01-10 DOI:10.1007/s40062-018-00229-6

Po Hu, Igor Kriz, Petr Somberg

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引用次数: 0

摘要

Bruner和Greenlees (The connective K-theory of finite groups, 2003)完整地计算了\(G=({\mathbb {Z}}/2)^n\)的连接k理论的Tate上同调(以及Borel上同调和上同调)。在这篇笔记中，我们用一种不同的，更基本的方法来重做计算，并将其扩展到\(p>2\) '。我们还确定了所得光谱，它是Eilenberg-Mac Lane光谱和有限个有限波斯特尼科夫塔的产物。对于\(p=2\)，我们也将我们的答案与[2]的结果完全一致，这是一种不同的形式，因此比较涉及一些非平凡组合。

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Tate cohomology of connected k-theory for elementary abelian groups revisited

Tate cohomology (as well as Borel homology and cohomology) of connective K-theory for \(G=({\mathbb {Z}}/2)^n\) was completely calculated by Bruner and Greenlees (The connective K-theory of finite groups, 2003). In this note, we essentially redo the calculation by a different, more elementary method, and we extend it to \(p>2\) prime. We also identify the resulting spectra, which are products of Eilenberg–Mac Lane spectra, and finitely many finite Postnikov towers. For \(p=2\), we also reconcile our answer completely with the result of [2], which is in a different form, and hence the comparison involves some non-trivial combinatorics.

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.