The sphere spectrum 
is the suspension spectrum of the based zero-dimensional
sphere 
.
Its sequential model has 
th space 
, with the usual suspension identifications. It is the unit
for the smash product, and its homotopy
groups are the stable homotopy groups
of spheres. The notation 
denotes its derived 
-completion.
Sphere Spectrum
See also
Bousfield Localization, Morava K-Theory, Stable Homotopy Group, Topological SpectrumExplore with Wolfram|Alpha
References
May, J. P. A Concise Course in Algebraic Topology. Chicago, IL: University of Chicago Press, 1999.Cite this as:
Weisstein, Eric W. "Sphere Spectrum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SphereSpectrum.html