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## The fundamental group of mapping torus [closed]

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.

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This question is more appropriate for math.stackexchange.com, so I'll answer it there. In general, I suggest that you give a question some time on math.stackexchange before moving it to MO. – HW May 17 2011 at 13:12