Mathematics Colloquia and Seminars

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A closed orientable 3-manifold can be constructed beginning with some 0-handles, add some 1-handles, then some 2-handles, them some more 1-handles, then some 2-handles, etc. and conclude by adding some 3-handles. The idea of thin position is to build the manifold as described before, with a succesion of 1-handles and 2-handles chosen to keep the boundaries of the intermediate steps as simple as possible. This idea was introduced by Scharlemann and Thompson. I will explain this idea, the properties of thin position and how it is related with heegaard splittings.