# Noetherian loop spaces

Natàlia Castellana; Juan Crespo; Jérôme Scherer

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 5, page 1225-1244
- ISSN: 1435-9855

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topCastellana, 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 -

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