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sphere spectrum
In stable homotopy theory, a branch of mathematics, the sphere spectrum ''S'' is the initial object in the categoty 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 .
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