K-theory Wang sequence of a mapping torus
= K-theory Wang sequence of a mapping torus
{c}
For a self-map $f:Z\to Z$, the mapping torus has an exact sequence containing
$$
K^{-1}(Z)\xrightarrow{1-f^*}K^{-1}(Z)
\longrightarrow K^0(T_f)
\longrightarrow K^0(Z)\xrightarrow{1-f^*}K^0(Z).
$$
If $K^{-1}(Z)=0$, then $K^0(T_f)\cong\ker(1-f^*:K^0(Z)\to K^0(Z))$.