  Given any connected topological space $X$, assume that there exists an
epimorphism $\phi: \pi_1(X) \to \mathbb{Z}$. The deck transformation group
$\mathbb{Z}$ acts on the associated infinite cyclic cover $X^\phi$ of $X$,
hence on the homology group $H_i(X^\phi, \mathbb{C})$. This action induces a
linear automorphism on the torsion part of the homology group as a module over
the Laurent ring $\mathbb{C}[t,t^{-1}]$, which is a finite dimensional
$\mathbb{C}$-vector space. We study the sizes of the Jordan blocks of this
linear automorphism. When $X$ is a compact K\"ahler manifold, we show that all
the Jordan blocks are of size one. When $X$ is a smooth complex
quasi-projective variety, we give an upper bound on the sizes of the Jordan
blocks, which is an analogue of the Monodromy Theorem for the local Milnor
fibration.
