## Abstract

This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological AndrÃ©-Quillen cohomology and of topological derivations are described. We give sample calculations of these cohomology theories and outline applications to the existence of $A_\infty$ and $E_\infty$ structures on various spectra. We also explain the relationship between topological derivations, spaces of multiplicative maps and moduli spaces of multiplicative structures.

Translated title of the contribution | Cohomology theories for highly structured ring spectra |
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Original language | English |

Title of host publication | Structured Ring Spectra |

Editors | Andrew Baker, Birgit Richter |

Publisher | Cambridge University Press |

Pages | 201 - 231 |

Volume | 315 |

ISBN (Print) | 0521603056 |

Publication status | Published - 2004 |