# Sphere spectrum

In stable homotopy theory, a branch of mathematics, the **sphere spectrum** *S* is the monoidal unit in the category of spectra. It is the suspension spectrum of *S*^{0}, i.e., a set of two points. Explicitly, the *n*th space in the sphere spectrum is the *n*-dimensional sphere *S*^{n}, and the structure maps from the suspension of *S*^{n} to *S*^{n+1} are the canonical homeomorphisms. The *k*-th homotopy group of a sphere spectrum is the *k*-th stable homotopy group of spheres.

The localization of the sphere spectrum at a prime number *p* is called the **local sphere** at *p* and is denoted by .

## References

- Adams, J. Frank (1974),
*Stable homotopy and generalised homology*, Chicago Lectures in Mathematics, University of Chicago Press, MR 0402720

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