Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory

摘要

We extend the theory of Thom spectra and the associated obstruction theory for orientations in order to support the construction of the E-infinity string orientation of tmf, the spectrum of topological modular forms. Specifically, we show that, for an E-infinity ring spectrum A, the classical construction of gl(1)A, the spectrum of units, is the right adjoint of the functor