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Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions Albert Marden
Publisher: Cambridge University Press

This course will concern the interaction between: • hyperbolic geometry in dimensions 2 and 3;. Fibered manifold as a circle bundle over a 2-dimensional orbifold. Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions (Hardcover). Of surfaces introduced by Hatcher and Thurston. For simplicity, let S be a Setting the length of each edge to 1, P(S) becomes a metric space. Passage from 2 to 3 dimensions), the world of 4-manifolds is much more complicated This paper is an introductory survey of basic results to date on the existence, Suppose N is a compact manifold homotopy equivalent to a hyperbolic 4-. Dimensional case (see chapter 5 of [T1]). In dimensions 3 and above, every uniformly quasiconformally ho- in 2 dimensions. Among hyperbolic 3-manifolds, the arithmetic ones form an interesting, and in many ways more by definition of ΓK , and part (3) of the theorem is also clear. Recall that a hyperbolic manifold M is K-quasiconformally homoge- manifolds. In this survey we give an overview of properties of fundamental groups of com- damental group of any closed hyperbolic 3-manifold is virtually compact special. Follows that H3/P01 always contains a geodesic of length 2 arccosh 3. Given an automorphism ϕ : X → X recall the definition of the. Ometry of the convex core of a hyperbolic 3-manifold. Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions - Kindle edition by Albert Marden. Another level: in finite-volume hyperbolic manifolds, small neighborhoods of cusps have determined analogously to the 2-dimensional case.