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28 March 2024
 
  » arxiv » 1411.7988

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A simple universal property of Thom ring spectra
Omar Antolín-Camarena ; Tobias Barthel ;
Date 28 Nov 2014
AbstractWe 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 $mathcal{O}$-monoidal functor. This allows us to relate Thom spectra to $mathbb{E}_n$-algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins--Mahowald theorem realizing $Hmathbb{F}_p$ as a Thom spectrum, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra.
Source arXiv, 1411.7988
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