Omar Antolin Camanera

The multiplicative structure of Thom spectra

Thom associated to each real vector bundle a space, now called its Thom space, and gave an isomorphism between its cohomology and the cohomology of the base of the bundle. For stable vector bundles or more generally stable spherical fibrations an analogous construction produces a Thom spectrum. In a paper of Ando, Blumberg, Hopkins, Gepner and Rezk a new approach to Thom spectra using the language of ∞-categories was introduced. Using their approach, we will explain how to apply some simple category theory to study multiplicative structures on Thom spectra, proving a generalization of Lewis's theorem that says that Thom spectra of n-fold loop maps are En-ring spectra and moreover characterizing this ring structure by a universal property.