Let $f\colon X\to X$ be a homeomorphism between a CW-complex $X$ and iteself.
Let $M_f=X\times [0,1]/(x,0)\sim (f(x),1)$, mapping torus of $X$ from $f$.
I want to calculate the fundamental group $\pi_1(M_f)$ of $M_f$ in terms of $\pi_1(X)$ and $f_*\colon \pi_1(X)\to \pi_1(X)$.
Are there any hint to do this?
p.s: This is not the homework problem.
This is the crossreference to this.