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By Bruno Martelli

This ebook offers a self-contained creation to the topology and geometry of surfaces and three-manifolds. the most objective is to explain Thurston's geometrisation of three-manifolds, proved via Perelman in 2002. The publication is split into 3 components: the 1st is dedicated to hyperbolic geometry, the second one to surfaces, and the 3rd to three-manifolds. It comprises entire proofs of Mostow's pressure, the thick-thin decomposition, Thurston's category of the diffeomorphisms of surfaces (via Bonahon's geodesic currents), the leading and JSJ decomposition, the topological and geometric category of Seifert manifolds, and Thurston's hyperbolic Dehn filling Theorem.

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