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|
|Title of host publication||Structured Ring Spectra|
|Editors||Andrew Baker, Birgit Richter|
|Publisher||Cambridge University Press|
|Pages||201 - 231|
|Publication status||Published - 2004|