2009/03/10 by Natalia Castellana, Natàlia Castellana, Castellana, Natalia +5
Mathematics · Medicine · #55P20 #55P35 #55P60 #55R35 #55S10 #55T10 #57T10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.AT #msc:55P20 #msc:55P35 #msc:55P60 #msc:55R35 #msc:55S10 #msc:55T10 #msc:57T10
paper · pdf · doi:10.48550/arxiv.0903.1701
23 pages
arxiv created 2009/03/10 · openalex publication_date 2009/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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^∞. 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.