Cohomology theories for highly structured ring spectra

Details Cohomology theories for highly structured ring spectra Cohomology theories for highly structured ring spectra

2002-11-18

arxiv.org/abs/math/0211275v1

Mathematics

Algebraic Topology

Scientific paper

This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-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.

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