诺特闭路空间
Noetherian loop spaces
摘要：
模p上同调是诺特的闭路空间的类比p-紧群的类大得多（对于p-紧群，模p上同调必须是有限的）。它包含Eilenberg-Mac Lane空间，如无限复射影空间和紧李群的3-连通覆盖。我们研究了这类对象的分类空间BX的上同调，证明了它和预期的一样小，即可以与BCP^ \infty的上同调相比较。我们还证明了BX与单个同伦群中p-紧群的分类空间基本不同。这特别适用于4-连通覆盖的分类空间的李群，并揭示了新的光如何上同调这样一个对象看起来像。
英文摘要：
The class of loop spaces whose mod p cohomology is Noetherian is much larger than the class of p-compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as the infinite complex projective space and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space BX of such an object and prove it is as small as expected, that is, comparable to that of BCP^\infty. We also show that BX differs basically from the classifying space of a p-compact group in a single homotopy group. This applies in particular to 4-connected covers of classifying spaces of Lie groups and sheds new light on how the cohomology of such an object looks like.
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