Lev Buhovsky

THE MASLOV CLASS OF LAGRANGIAN TORI AND QUANTUM PRODUCTS IN FLOER COHOMOLOGY

We use Floer cohomology to prove the monotone version of a conjecture of Audin: the minimal Maslov number of a monotone Lagrangian torus in ℝ2n is 2. Our approach is based on the study of the quantum cup product on Floer cohomology and in particular the behavior of Ohs spectral sequence with respect to this product. As further applications, we prove existence of holomorphic disks with boundaries on Lagrangians as well as new results on Lagrangian intersections.

Homology of Lagrangian submanifolds in cotangent bundles

In this paper we find homological restrictions on Lagrangians in cotangent bundles of spheres and Lens spaces.

On the Uniqueness of Hofer’s Geometry

We study the class of pseudo-norms on the space of smooth functions on a closed symplectic manifold, which are invariant under the action of the group of Hamiltonian diffeomorphisms. Our main result shows that any such pseudo-norm that is continuous with respect to the C∞-topology, is dominated from above by the L∞-norm. As a corollary, we obtain that any bi-invariant Finsler pseudo-metric on the group of Hamiltonian diffeomorphisms that is generated by an invariant pseudonorm that satisfies the aforementioned continuity assumption, is either identically zero or equivalent to Hofer’s metric.

Towards the C0 flux conjecture

In this note, we generalise a result of Lalonde, McDuff and Polterovich concerning the

Towards the C^0 flux conjecture

C^0

Nonisometric Domains with the Same Marvizi – Melrose Invariants

flux conjecture, thus confirming the conjecture in new cases of a symplectic manifold. Also, we prove the continuity of the flux homomorphism on the space of smooth symplectic isotopies endowed with the

A \(C^0\) counterexample to the Arnold conjecture

C^0

UNBOUNDEDNESS OF THE FIRST EIGENVALUE OF THE LAPLACIAN IN THE SYMPLECTIC CATEGORY

topology, which implies the

Poisson brackets and symplectic invariants

C^0

Uniqueness of generating Hamiltonians for topological Hamiltonian flows

rigidity of Hamiltonian paths, conjectured by Seyfaddini.