The spectra ko and ku are not Thom spectra: an approach using THH

Abstract

The construction of various bordism theories as Thom spectra served as a motivating example for the development of highly structured ring spectra. Various other examples of Thom spectra followed; for instance, various Eilenberg–MacLane spectra are known to be constructed in this way (see Mahowald [5]). However, Mahowald [6] proved that the connective K–theory spectra ko and ku are not the 2–local Thom spectra of any vector bundles, and that the spectrum ko is not the Thom spectrum of a spherical fibration classified by a map of H-spaces. Rudyak [7] later proved that ko and ku are not Thom spectra p–locally at odd primes p .