Berlin-Hamburg-Hannover-Seminar am 09.01.2026

Fabio Gironella (Nantes) Vanishing cycles for symplectic foliations

Taut codimension-1 foliations are notoriously rigid in ambient dimension 3: as proved by Novikov '64, they give for instance non-trivial topological constraints on the ambient manifold. In higher ambient dimensions, this kind of foliations is on the other hand extremely flexible, and satisfies an h-principle. Strong symplectic foliations are a natural high-dimensional generalization of 3-dimensional taut foliations that instead behave much more rigidly, i.e. in a geometrically interesting way. One of the reasons for this rigidity is that symplectic techniques such as pseudo-holomorphic curves à la Gromov work well for strong symplectic foliations. I will present a joint work with Klaus Niederkrüger and Lauran Toussaint, where we give a new obstruction for a symplectic foliation to be strong. This comes in the form of a Lagrangian high-dimensional version of vanishing cycles for smooth codimension 1 foliations on 3-manifolds, which are known not to exist in the taut case due to a famous work of Novikov. The proof relies exactly on pseudo-holomorphic curve techniques, in a way which is parallel to the case of the Plastikstufe introduced by Niederkrüger '06 in the contact setting.

Thomas Massoni (Stanford) Symplectic rigidity of Anosov flows under orbit equivalence

A classical construction of Mitsumatsu, later generalized by Hozoori, associates to any (oriented) Anosov flow on a closed 3-manifold M a Liouville structure on the thickening [-1,1] x M. This construction also extends to suitable taut foliations. From the dynamical viewpoint, it is natural to study Anosov flows up to orbit equivalence, i.e., homeomorphisms sending (unparametrized) orbits to orbits. Such maps are typically not smooth, so the effect on the associated Liouville structures is far from obvious. In this talk, I will present joint work with Jonathan Bowden showing that orbit equivalent Anosov flows induce exact symplectomorphic Liouville structures. A similar result holds for taut foliations. Consequently, the symplectic invariants (Floer homology, Fukaya category, etc.) attached to Anosov flows are preserved under orbit equivalence.