Sphere spectrum

From formulasearchengine
Jump to navigation Jump to search

In stable homotopy theory, a branch of mathematics, the sphere spectrum S is the smallest nontrivial spectrum. It is the suspension spectrum of S0, i.e., a set of two points. Explicitly, the nth space in the sphere spectrum is the n-dimensional sphere Sn, and the structure maps from the suspension of Sn to Sn+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 .


  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}