Noetherian loop spaces

  • Jérôme Scherer

    EPFL, Lausanne, Switzerland
  • Natàlia Castellana Vila

    Universidad Autonoma de Barcelona, Bellaterra, Spain
  • Juan A. Crespo

    Universidad Autónoma de Madrid, Spain


The class of loop spaces of which the mod pp cohomology is Noetherian is much larger than the class of pp-compact groups (for which the mod pp cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as CP\mathbb C P^\infty and 33-connected covers of compact Lie groups. We study the cohomology of the classifying space BXBX of such an object and prove it is as small as expected, that is, comparable to that of BCPB\mathbb C P^\infty. We also show that BXBX differs basically from the classifying space of a pp-compact group in a single homotopy group. This applies in particular to 44-connected covers of classifying spaces of compact Lie groups and sheds new light on how the cohomology of such an object looks like.

Cite this article

Jérôme Scherer, Natàlia Castellana Vila, Juan A. Crespo, Noetherian loop spaces. J. Eur. Math. Soc. 13 (2011), no. 5, pp. 1225–1244

DOI 10.4171/JEMS/279