A simple universal property of Thom ring spectra. Issue 1 (31st October 2018)

• Record Type: Journal Article
• Authors: Antolín‐Camarena, Omar; Barthel, Tobias
• Is Part Of: Journal of topology. Volume 12:Issue 1(2019)
• Page Start: 56
• Page End: 78
• Publication Date: 2018-10-31
• Subjects: 55N20 -- 55P42 -- 55P43 -- 55P48 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12084
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: 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 E n ‐algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins–Mahowald theorem realizing H F p and H Z as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra.