Wang sequence
= Wang sequence
{c}
{wiki}
For the mapping torus of $f:F\to F$, the Wang exact sequence contains
$$
\cdots\to H_q(F)\xrightarrow{1-f_*}H_q(F)\to H_q(T_f)\to H_{q-1}(F)\xrightarrow{1-f_*}H_{q-1}(F)\to\cdots.
$$
= Wang sequence
{c}
{wiki}
For the mapping torus of $f:F\to F$, the Wang exact sequence contains
$$
\cdots\to H_q(F)\xrightarrow{1-f_*}H_q(F)\to H_q(T_f)\to H_{q-1}(F)\xrightarrow{1-f_*}H_{q-1}(F)\to\cdots.
$$