# Cohomology theories for highly structured ring spectra

A Lazarev

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

## 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 English Structured Ring Spectra Andrew Baker, Birgit Richter Cambridge University Press 201 - 231 315 0521603056 Published - 2004

### Bibliographical note

Other: LMS Lecture Notes series