Geometry and Topology Seminar

The question about existence and uniqueness (up to deformation) of taut foliations on a three manifold has been studied for decades. Obstructions for existence of taut foliations on rational homology spheres have been obtained by considering the perturbations of the foliation to contact structures. Recently, by showing that the perturbed contact structure is unique in many cases, Vogel and Bowden constructed examples of taut foliations that are homotopic as distributions but can not be deformed to each other through taut foliations. In this talk I will introduce a new approach to this problem. Instead of perturbing the foliation to a contact structure, we directly study a symplectization of the foliation itself, and that leads to a canonically defined class in the monopole Floer homology. Then I will apply this idea to the questions of existence and uniqueness of taut foliations.