Title: An obstruction to planarity of contact 3-manifolds

Abstract: We give new obstructions to the existence of planar open
books on contact structures, in terms of the homology of their
fillings. I will talk about applications to links of surface
singularities, Seifert fibred spaces, and integer homology spheres.
This is joint work with Paolo Ghiggini and Olga Plamenevskaya.