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Presentations of 3-manifolds and related invariants
Institut de Mathématiques de Bourgogne - UMR 5584 CNRS
Université de Bourgogne
9 avenue Alain Savary
21078 DIJON Cedex
One historical achievement of (differential) topology is the solution of the classification problem for high-dimensional manifolds (dim > 5). We are mainly left to the study of dimension 3 and 4. In order to study 3-manifolds, we want to give a good way of constructing it, especially leading to combinatorial contexts. I will sum up some presentations of 3-manifolds (by Heegard splitting, by Dehn surgery... etc.). This presentation allows us to define invariants in a natural way, making interesting links between 3-dimensional topology and other fields such as algebra (through Mapping Class groups of surfaces) and Knot theory (Kirby moves). If I have enough time, i will then give details about this invariant, and try to introduce ongoing problematics about these subjects.