We give a survey of a generalization of Quillen–Sullivan rational homotopy theory which gives spectral algebra models of unstable vn-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 André-Quillen cohomology, Koszul duality, and Goodwillie calculus.
CITATION STYLE
Behrens, M., & Rezk, C. (2020). Spectral algebra models of unstable vn-Periodic Homotopy Theory. In Springer Proceedings in Mathematics and Statistics (Vol. 309, pp. 275–323). Springer. https://doi.org/10.1007/978-981-15-1588-0_10
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