An Orientation Map for Height p-1 Real E Theory

Abstract

Let be an odd prime and let = ℎ −1 be the fixed points of height − 1 Morava theory. We say that a spectrum has algebraic theory if the splitting of * ( ) as an * [ ]-module lifts to a topological splitting of ∧ . We develop criteria to show that a spectrum has algebraic theory, in particular showing that any connective spectrum with mod homology concentrated in degrees 2 ( − 1) has algebraic theory. As an application, we answer a question posed by Hovey and Ravenel [9] by producing a unital orientation 4 −4 → analogous to the orientation of at = 2.