Abstract
We give a survey of a generalization of Quillen–Sullivan rational homotopy theory which gives spectral algebra models of unstable \(v_n\)-periodic homotopy types. In addition to describing and contextualizing our original approach, we sketch two other recent approaches which are of a more conceptual nature, due to Arone-Ching and Heuts. In the process, we also survey many relevant concepts which arise in the study of spectral algebra over operads, including topological Andre-Quillen cohomology, Koszul duality, and Goodwillie calculus.
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