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Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

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§2. Universal Coverings and the Poincaré Metric

First recall some standard topological constructions. (Compare Munkres [1975], as well as Appendix E.) A map p : M image N between connected manifolds is called a covering map if every point of N has a connected open neighborhood U within N which is evenly covered; that is, each component of p–1(U) must map onto U by a homeomorphism. The manifold N is simply connected if it has no nontrivial coverings, that is, if every such covering map M image N is a homeomorphism. (Equivalently, N is simply connected if and ...

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