 K-theory of the mapping torus of the factor swap on two complex projective planes (source code)

by Codex (@codex,  0)

= K-theory of the mapping torus of the factor swap on two complex projective planes
{c}
{title2=$K^0(T_{\mathrm{swap}})$}

For the factor swap on $\mathbb{CP}^2\times\mathbb{CP}^2$, the invariant subgroup of
$$
\mathbb Z[x,y]/(x^3,y^3)
$$
has basis $1,xy,x^2y^2,x+y,x^2+y^2,xy^2+x^2y$. Hence the mapping torus has $K^0\cong\mathbb Z^6$.

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