TL;DR
This paper investigates free global spectra, revealing their rarity and specific properties, and demonstrates that certain universal spectra lack a global refinement, highlighting limitations in their structure.
Contribution
It introduces the concept of free global spectra, analyzes their existence and properties, and applies these findings to show the non-existence of a global refinement for universal free G-spectra.
Findings
Free global spectra often do not exist.
When they exist, their homotopy groups satisfy strong divisibility conditions.
The universal free G-spectrum EG+ does not admit a global refinement.
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 -spectrum does not admit a global refinement.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems