Conventions

• The term “ring spectrum” refers to homotopy ring spectrum.

• If $X$ is a based space, we will denote $\Sigma ^\infty X$ by $X$ again. Thus, $E_*(X)$ is always reduced homology.

• If $X$ is an unbased space, we will denote $\Sigma ^\infty _+ X$ by $X_+$. Thus, $E_*(X_+)$ is unreduced homology.