Title: From Poincaré to Thurston
Speaker: Parsa Mashaykehi
Abstract: The classification problem of manifolds is one of the main questions in topology. The answer was known for dimension 2 by the end of the 19th century and there is no hope of classifying all manifolds in dimensions more than 3. The Poincaré conjecture was an important step towards the classification of 3-manifolds. Thurston proposed the geometrization conjecture, which is stronger than the Poincaré conjecture and is an almost complete answer to the classification of 3-manifolds. Both conjectures were proved by Perelman in 2002-3. In this talk, we also discuss about the generalized and smooth Poincaré conjectures. In the end, we see how the geometrization conjecture implies the Poincaré conjecture and why the fundamental group is almost a full invariant for 3-manifolds.
Some snacks will be provided before and after the talk.