# 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 contribution Spaces of multiplicative maps between highly structured ring spectra English Categorical Decomposition Techniques in Algebraic Topology, International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 Arone , G.; Hubbuck, J.; Levi, M R.; Weiss Birkhäuser Basel 237 - 259 215 3764304006 Published - 2004

### Bibliographical note

Other: Progress in Mathematics series