Commuting homotopy limits and smash products
Commuting homotopy limits and smash products
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通勤同伦极限，粉碎产品
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Marco Varisco
中科院分区：
文献类型：
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作者：
W. Lueck;H. Reich;Marco Varisco
一般说来，取谱图的同伦逆极限和用固定空间粉碎谱的过程是不可交换的。在这篇文章中，我们调查了这两个过程在哪些额外的假设下确实可以通勤。事实上，我们处理的是一个等变的推广，它涉及离散群的轨道范畴上的谱和粉碎积。如果研究与拓扑环同调相关的等变同调理论，这种情况自然会发生。本文的主要定理将把Boekstedt，Hsiang和Madsen关于代数K-理论Novikov猜想的结果推广到虚循环子群族的集合映射上。
In general the processes of taking a homotopy inverse limit of a diagram of spectra and smashing spectra with a fixed space do not commute. In this paper we investigate under what additional assumptions these two processes do commute. In fact we deal with an equivariant generalization which involves spectra and smash products over the orbit category of a discrete group. Such a situation naturally occurs if one studies the equivariant homology theory associated to topological cyclic homology. The main theorem of this paper will play a role in the generalization of the results obtained by Boekstedt, Hsiang and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map for the family of virtually cyclic subgroups.