Open book decompositions of 3-manifolds are a topological construction that was recently shown to be very useful in studying geometric phenomena. In particular, Giroux proved in 2000 that open book decompositions of a 3-manifold are in 1-1 correspondence with its contact structures. I will introduce open book decompositions, state some properties, and if there is time say how they relate to contact structures.
The talk should be accessible to everybody (elementary geometry and topology required).