## Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy

Autor(en): | Baues, Hans-Joachim Frankland, Martin |

Stichwörter: | A-infinity morphism; distributivity up to homotopy; Eilenberg-MacLane spectrum; higher co-homology operation; Higher distributivity; homotopy invariant; Kristensen derivation; mapping algebra; mapping theory; Mathematics; Steenrod algebra; topological abelian group |

Erscheinungsdatum: | 2017 |

Herausgeber: | ELECTRONIC JOURNALS PROJECT |

Journal: | NEW YORK JOURNAL OF MATHEMATICS |

Volumen: | 23 |

Startseite: | 1539 |

Seitenende: | 1580 |

Zusammenfassung: | Primary cohomology operations, i.e., elements of the Steen-rod algebra, are given by homotopy classes of maps between Eilenberg-MacLane spectra. Such maps (before taking homotopy classes) form the topological version of the Steenrod algebra. Composition of such maps is strictly linear in one variable and linear up to coherent homotopy in the other variable. To describe this structure, we introduce a hierarchy of higher distributivity laws, and prove that the topological Steenrod algebra satisfies all of them. We show that the higher distributivity laws are homotopy invariant in a suitable sense. As an application of 2-distributivity, we provide a new construction of a derivation of degree -2 of the mod 2 Steenrod algebra. |

ISSN: | 10769803 |

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