## 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 |
---|---|

Original language | English |

Title of host publication | Categorical Decomposition Techniques in Algebraic Topology, International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 |

Editors | Arone , G.; Hubbuck, J.; Levi, M R.; Weiss |

Publisher | Birkhäuser Basel |

Pages | 237 - 259 |

Volume | 215 |

ISBN (Print) | 3764304006 |

Publication status | Published - 2004 |