In mathematics, particularly in the field of algebraic topology, the concept of a "sphere spectrum" refers to a particular type of structured object that arises in stable homotopy theory. The sphere spectrum is a central object that provides a foundation for the study of stable homotopy groups of spheres, stable cohomology theories, and many other constructions in stable homotopy. To understand the sphere spectrum, it's helpful to start with the notion of spectra in stable homotopy theory.
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The sphere spectrum is . It is the unit of the smash product of spectra. Its integer suspensions of spectra represent stable homotopy groups.