Commutative Γ-Rings do not model all commutative ring spectra

Tyler Lawson

doi:10.4310/HHA.2009.v11.n2.a9

Commutative Γ-Rings do not model all commutative ring spectra

Tyler Lawson

School of Mathematics

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

4 Scopus citations

Abstract

We show that the free E_∞-algebra on a zero-cell cannot be modeled by a commutative Γ-ring. The proof shows that Dyer-Lashof operations of positive degree must vanish on the zero'th homology of such an object.

Original language	English (US)
Pages (from-to)	189-194
Number of pages	6
Journal	Homology, Homotopy and Applications
Volume	11
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2009.v11.n2.a9
State	Published - 2009

Keywords

Dyer-Lashof operation
Gamma-space
Ring spectrum

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10.4310/HHA.2009.v11.n2.a9

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title = "Commutative Γ-Rings do not model all commutative ring spectra",

abstract = "We show that the free E∞-algebra on a zero-cell cannot be modeled by a commutative Γ-ring. The proof shows that Dyer-Lashof operations of positive degree must vanish on the zero'th homology of such an object.",

keywords = "Dyer-Lashof operation, Gamma-space, Ring spectrum",

author = "Tyler Lawson",

year = "2009",

doi = "10.4310/HHA.2009.v11.n2.a9",

language = "English (US)",

volume = "11",

pages = "189--194",

journal = "Homology, Homotopy and Applications",

issn = "1532-0073",

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PY - 2009

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AB - We show that the free E∞-algebra on a zero-cell cannot be modeled by a commutative Γ-ring. The proof shows that Dyer-Lashof operations of positive degree must vanish on the zero'th homology of such an object.

KW - Dyer-Lashof operation

KW - Gamma-space

KW - Ring spectrum

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DO - 10.4310/HHA.2009.v11.n2.a9

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SN - 1532-0073

VL - 11

SP - 189

EP - 194

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

IS - 2

ER -

Commutative Γ-Rings do not model all commutative ring spectra

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Keywords

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