A monopole invariant for foliations without transverse invariant measure

A monopole invariant for foliations without transverse invariant measure

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Boyu Zhang , Harvard University
Fine Hall 314

The question about existence and flexibility of taut foliations on a three manifold has been studied for decades. Floer-theoretical obstructions for the existence of taut foliations on rational homology spheres have been obtained by Kronheimer, Mrowka, Ozsvath, and Szabo by perturbing 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 we will propose a different approach. 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 we will apply this idea to the questions of existence and flexibility of taut foliations.