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Mathematics, Algebraic Topology
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
$\mathcal{O}$-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
$H\mathbb{F}_p$ and $H\mathbb{Z}$ as Thom spectra, and compute the topological
Hochschild homology and the cotangent complex of various Thom spectra.
