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Adams operation and the boundary pushforward of a sphere bundle

{c}
{title2=$\psi^2:K^{-1}(S(\gamma\oplus\gamma))\to K^{-1}(S(\gamma\oplus\gamma))$}

Choose $a,b$ with $p_!(a)=t^{n-1}$ and $p_!(b)=t^n$, where $t=1-[\overline\gamma]$. Then
$$
\psi^2(a)=2^{n+1}a-(n+1)2^n b,
\qquad
\psi^2(b)=2^{n+2}b.
$$


Second Adams operation on the odd K-theory of the sphere bundle of two tautological lines

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 142 / 4 / Solution

Second Adams operation on the odd K-theory of the sphere bundle of two tautological lines ( $ψ^{2} : K^{- 1} (S (γ \oplus γ)) \to K^{- 1} (S (γ \oplus γ))$ )

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Second Adams operation on the odd K-theory of the sphere bundle of two tautological lines (ψ2:K−1(S(γ⊕γ))→K−1(S(γ⊕γ)))

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Second Adams operation on the odd K-theory of the sphere bundle of two tautological lines ( $ψ^{2} : K^{- 1} (S (γ \oplus γ)) \to K^{- 1} (S (γ \oplus γ))$ )

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