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Topological K-theory

Bott isomorphism

{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

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 142 / 2 / Solution

Complex K-theory of a sphere ( $K^{i} (S^{d})$ )

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Complex K-theory of a sphere (Ki(Sd))

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