Noetherian loop spaces

Castellana, Natàlia, Crespo, Juan, and Scherer, Jérôme. "Noetherian loop spaces." Journal of the European Mathematical Society 013.5 (2011): 1225-1244. <http://eudml.org/doc/277234>.

@article{Castellana2011,
abstract = {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 $B$X 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.},
author = {Castellana, Natàlia, Crespo, Juan, Scherer, Jérôme},
journal = {Journal of the European Mathematical Society},
keywords = {Lie group; loop space; Noetherian algebra; $p$-compact group; Steenrod algebra; Lannes’ $T$-functor; Krull filtration; Eilenberg-Mac Lane space; Serre spectral sequence; compact Lie group; loop space; Noetherian algebra; -compact group; Steenrod algebra; Lannes’ -functor; Krull filtration; Eilenberg-Mac Lane space; Serre spectral sequence},
language = {eng},
number = {5},
pages = {1225-1244},
publisher = {European Mathematical Society Publishing House},
title = {Noetherian loop spaces},
url = {http://eudml.org/doc/277234},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Castellana, Natàlia
AU - Crespo, Juan
AU - Scherer, Jérôme
TI - Noetherian loop spaces
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 5
SP - 1225
EP - 1244
AB - 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 $B$X 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.
LA - eng
KW - Lie group; loop space; Noetherian algebra; $p$-compact group; Steenrod algebra; Lannes’ $T$-functor; Krull filtration; Eilenberg-Mac Lane space; Serre spectral sequence; compact Lie group; loop space; Noetherian algebra; -compact group; Steenrod algebra; Lannes’ -functor; Krull filtration; Eilenberg-Mac Lane space; Serre spectral sequence
UR - http://eudml.org/doc/277234
ER -