On the cohomology of highly connected covers of finite Hopf spaces

Natàlia Castellana; Juan A. Crespo; Jérôme Scherer

doi:10.1016/j.aim.2007.03.011

On the cohomology of highly connected covers of finite Hopf spaces

Natàlia Castellana, Juan A. Crespo, Jérôme Scherer

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

Relying on the computation of the André-Quillen homology groups for unstable Hopf algebras, we prove that if the mod p cohomology of both the fiber and the base in an H-fibration is finitely generated as algebra over the Steenrod algebra, then so is the mod p cohomology of the total space. In particular, the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra. © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	250-262
Journal	Advances in Mathematics
Volume	215
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2007.03.011
Publication status	Published - 20 Oct 2007

Keywords

André-Quillen homology
Eilenberg-Moore spectral sequence
Fibrations
H-space
Steenrod algebra

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abstract = "Relying on the computation of the Andr{\'e}-Quillen homology groups for unstable Hopf algebras, we prove that if the mod p cohomology of both the fiber and the base in an H-fibration is finitely generated as algebra over the Steenrod algebra, then so is the mod p cohomology of the total space. In particular, the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

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AU - Castellana, Natàlia

AU - Crespo, Juan A.

AU - Scherer, Jérôme

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N2 - Relying on the computation of the André-Quillen homology groups for unstable Hopf algebras, we prove that if the mod p cohomology of both the fiber and the base in an H-fibration is finitely generated as algebra over the Steenrod algebra, then so is the mod p cohomology of the total space. In particular, the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra. © 2007 Elsevier Inc. All rights reserved.

AB - Relying on the computation of the André-Quillen homology groups for unstable Hopf algebras, we prove that if the mod p cohomology of both the fiber and the base in an H-fibration is finitely generated as algebra over the Steenrod algebra, then so is the mod p cohomology of the total space. In particular, the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra. © 2007 Elsevier Inc. All rights reserved.

KW - André-Quillen homology

KW - Eilenberg-Moore spectral sequence

KW - Fibrations

KW - H-space

KW - Steenrod algebra

U2 - 10.1016/j.aim.2007.03.011

DO - 10.1016/j.aim.2007.03.011

M3 - Article

VL - 215

SP - 250

EP - 262

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

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