A simple universal property of Thom ring spectra

By Omar Antol'in-Camarena, T. Barthel. Journal of Topology, 2014

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We give a simple universal property of the multiplicative structure on the Thom spectrum of an n ‐fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax O ‐monoidal functor. This allows us to relate Thom spectra to En ‐algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins–Mahowald theorem realizing HFp and HZ as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bf11f3175da82291639e2802fc4b612603ec01cd