Complex K-theory of a sphere
= Complex K-theory of a sphere
{c}
{title2=$\widetilde K^i(S^d)$}
Complex Bott periodicity gives
$$
\widetilde K^i(S^d)\cong
\begin{cases}
\mathbb Z,&i-d\text{ is even},\\
0,&i-d\text{ is odd}.
\end{cases}
$$
= Complex K-theory of a sphere
{c}
{title2=$\widetilde K^i(S^d)$}
Complex Bott periodicity gives
$$
\widetilde K^i(S^d)\cong
\begin{cases}
\mathbb Z,&i-d\text{ is even},\\
0,&i-d\text{ is odd}.
\end{cases}
$$