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Spaces of multiplicative maps between highly structured ring spectra

2002/09/27 by A. Lazarev, А. Н. Лазарев, Lazarev, A.
Mathematics · #55N20 #55P42 #55S37 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.AT #math.KT #msc:55N20 #msc:55P42 #msc:55S37

paper · pdf · doi:10.48550/arxiv.math/0209388

arxiv created 2002/09/27 · openalex publication_date 2002/09/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We uncover a somewhat surprising connection between spaces of multiplicative maps between A_∞-ring spectra and topological Hochschild cohomology. As a consequence we show that such spaces become infinite loop spaces after looping only once. We also prove that any multiplicative cohomology operation in complex cobordisms theory MU canonically lifts to an A_∞-map MU→ MU. This implies, in particular, that the Brown-Peterson spectrum BP splits off MU as an A_∞-ring spectrum.

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