Infinite cyclic cover corresponding to non-zero cohomology class $alpha in H^1(x,mathbb Z)$
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I want to understand the following sentence: Let X a compact (complex) manifold which has a non-zero cohomology class $alpha in H^1(X,mathbb Z)$ . Let $pi: bar Xto X$ be the corresponding infinite cyclic covering. What does this mean? It seems that an infinite cyclic covering is a cover with fiber $mathbb Z$ . But why does such a covering exist, and how is it related to the cohomology class?
geometry differential-geometry algebraic-topology complex-geometry covering-spaces
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edited Jan 1 at 15:41
klirk
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