A diary
Ad 2:
2020-02-04 16:23:40 (UTC)

Some notes

Since the time of Henry Poincare, it has been known that each closed, orientable surface of genus at least 2 admits a hyperbolic Riemannian metric. We fix such a 2-manifold S with universal covering projection p from the hyperbolic plane to S, p a local isometry. The standard identification of the fundamental group of S with the group of covering translations of the universal cover of S gives a discrete faithful representation. Note that, a representation of a group is faithful if it is one-to-one. A representation of a group is discrete if the range of the group is a discrete set in the codomain of the representation. The representation is a map from a group to a group of linear maps acting on

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