Classifying spectra of saturated fusion systems
Classifying spectra of saturated fusion systems
复制标题
饱和聚变系统的分类谱
DOI：
10.2140/agt.2006.6.195
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发表时间：
2005
影响因子：
0.7
通讯作者：
Kári Ragnarsson
中科院分区：
文献类型：
--
作者：
Kári Ragnarsson
将光谱分类分配给饱和聚变系统是由 Linckelmann 和 Webb 提出的，并由 Broto、Levi 和 Oliver 实施。本文给出了更严格（但等效）的分类谱结构。结果表明，该分配对于保融合同态来说是函子，其方式是将稳定的 p 完全分类空间的分配扩展到有限群，并承认类似于有限群的转移理论。此外，还描述了分类谱之间的同伦类映射组，特别是表明，可以从其分类谱（被视为基础 p 群稳定分类空间下的对象）来重建融合系统。 55R35； 20D20、55P42
The assignment of classifying spectra to saturated fusion systems was suggested by Linckelmann and Webb and has been carried out by Broto, Levi and Oliver. A more rigid (but equivalent) construction of the classifying spectra is given in this paper. It is shown that the assignment is functorial for fusion-preserving homomorphisms in a way which extends the assignment of stable p‐completed classifying spaces to finite groups, and admits a transfer theory analogous to that for finite groups. Furthermore the group of homotopy classes of maps between classifying spectra is described, and in particular it is shown that a fusion system can be reconstructed from its classifying spectrum regarded as an object under the stable classifying space of the underlying p‐group. 55R35; 20D20, 55P42