5 papers
On the Hofer-Zehnder conjecture for semipositive symplectic manifolds
Marcelo S. Atallah, Han Lou
We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homol…
On the spectral diameter of the Grassmannians
Habib Alizadeh, Marcelo S. Atallah, Dylan Cant +1
The diameter of the spectral pseudometric on the universal cover of the Hamiltonian diffeomorphism group of is shown to be finite whenever is a prime number.…
Weinstein exactness of nearby Lagrangians and related questions
Marcelo S. Atallah, Jean-Philippe Chassé, Rémi Leclercq +1
We address the following problem: if a Hamiltonian diffeomorphism maps a Lagrangian submanifold to a small Weinstein neighborhood of , is the image necessarily Hamiltonian i…
-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces
Marcelo Atallah, Cheuk Yu Mak, Weiwei Wu
We investigate the -topology of the group of symplectic diffeomorphisms of positive symplectic rational surfaces. For all but a few exceptions, we prove that the group of Hami…
The number of periodic points of surface symplectic diffeomorphisms
Marcelo S. Atallah, Marta Batoréo, Brayan Ferreira
We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus ; it implies that a symplectic diffeomorphism isotopic…