Spaces of multiplicative maps between highly structured ring spectra

A Lazarev

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

Abstract

We uncover a somewhat surprising connection between spaces of multiplicative maps between $A_\infty$-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 $A_\infty$-map $MU\to MU$. This implies, in particular, that the Brown-Peterson spectrum $BP$ splits off $MU$ as an $A_\infty$-ring spectrum.
Translated title of the contributionSpaces of multiplicative maps between highly structured ring spectra
Original languageEnglish
Title of host publicationCategorical Decomposition Techniques in Algebraic Topology, International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001
EditorsArone , G.; Hubbuck, J.; Levi, M R.; Weiss
PublisherBirkhäuser Basel
Pages237 - 259
Volume215
ISBN (Print)3764304006
Publication statusPublished - 2004

Bibliographical note

Other: Progress in Mathematics series

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