K-theory spectrum
From HandWiki
In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum [math]\displaystyle{ K_R }[/math] whose nth term is given by, writing [math]\displaystyle{ \Sigma R }[/math] for the suspension of R,
- [math]\displaystyle{ (K_R)_n = K_0(\Sigma^n R) \times BGL(\Sigma^n R)^+ }[/math],
where "+" means the Quillen's + construction.[1] By definition, [math]\displaystyle{ K_i(R) = \pi_i(K_R) }[/math].
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