On free global spectra

Abstract

In this note we define and study free global spectra: global spectra with non-trivial geometric fixed points only at the trivial group. We show that free global spectra often do not exist, and when they do, their homotopy groups satisfy strong divisibility conditions. As an application, we show that the universal free $G$-spectrum $E{G}_{+}$ does not admit a global refinement.

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