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 formula_1.