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The geometrisation of 3-manifolds

Bruno Martelli
Institution: 
UNIPI
Schedule: 
Wednesday, October 27, 2021 - 17:00 to 18:00
Location: 
A-005
Abstract: 

We will describe the geometrisation of three-manifolds, conjectured by Thurston in the early 80s and proved by Perelman twenty years later. The geometrisation theorem asserts that every 3-manifold decomposes into canonical pieces, each of which admits a particularly nice Riemannian metric. We will explain the precise meaning of this theorem, including the words "decomposes", "canonical pieces", and "particularly nice". At the end we will briefly discuss the (yet mostly unknown) role of hyperbolic geometry in dimension higher than 3.

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