Journal of the European Mathematical Society
Full-Text PDF (239 KB) | Metadata | Table of Contents | JEMS summary
Published online: 2011-07-13
Noetherian loop spacesNatàlia Castellana, Juan A. Crespo and Jérôme Scherer (1) Universidad Autonoma de Barcelona, Bellaterra, Spain
(2) Universidad Autónoma de Madrid, Spain
(3) EPFL, Lausanne, Switzerland
The class of loop spaces of which the 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 $\mathbb C P^\infty$ 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 $B\mathbb C P^\infty$. 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 compact Lie groups and sheds new light on how the cohomology of such an object looks like.
No keywords available for this article.
Castellana Natàlia, Crespo Juan, Scherer Jérôme: Noetherian loop spaces. J. Eur. Math. Soc. 13 (2011), 1225-1244. doi: 10.4171/JEMS/279