An Orientation Map for Height p-1 Real E Theory

2019/08/30 by Chatham, Hood
#55N22 (Secondary) #55P42 (Primary) 55N20 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.11496

Abstract

Let p be an odd prime and let EO = E_p-1^hC_p be the C_p fixed points of height p-1 Morava E theory. We say that a spectrum X has algebraic EO theory if the splitting of K_*(X) as an K_*[C_p]-module lifts to a topological splitting of EO \wedge X. We develop criteria to show that a spectrum has algebraic EO theory, in particular showing that any connective spectrum with mod p homology concentrated in degrees 2k(p - 1) has algebraic EO theory. As an application, we answer a question posed by Hovey and Ravenel by producing a unital orientation MY_4p-4→ EO analogous to the MSU orientation of KO at p=2.

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