25 citations · 81 across the 17 of their papers we have counts for
18 papers · 1 filter
Hofer-continuous quasi-morphisms on Liouville manifolds
Frol Zapolsky
We show that, given a complete Liouville manifold, any homogeneous quasi-morphism on its Hamiltonian group, which satisfies a strengthened version of Hofer continuity called stabil…
On the Lagrangian Hofer geometry of Clifford tori
Frol Zapolsky
We show that the space of Lagrangians which are Hamiltonian isotopic to the Clifford torus in a complex projective space or in the four-dimensional quadric, taken with Chekanov's L…
Constraints on symplectic quasi-states
Adi Dickstein, Frol Zapolsky
We prove that given a closed connected symplectic manifold equipped with a Borel probability measure, an arbitrarily large portion of the measure can be covered by a symplectically…
Symplectic topology and ideal-valued measures
Adi Dickstein, Yaniv Ganor, Leonid Polterovich +1
We adapt Gromov's notion of ideal-valued measures to symplectic topology, and use it for proving new results on symplectic rigidity and symplectic intersections. Furthermore, it en…
Quasi-morphisms on contactomorphism groups and Grassmannians of 2-planes
Frol Zapolsky
We construct a natural prequantization space over a monotone product of a toric manifold and an arbitrary number of complex Grassmannians of 2-planes in even-dimensional complex sp…
Rigidity of the L^p norm of the Poisson bracket on surfaces
Karina Samvelyan, Frol Zapolsky
For a symplectic manifold let be the corresponding Poisson bracket. In this note we prove that the functional is lower-se…
On the contact mapping class group of the contactization of the - Milnor fiber
Sergei Lanzat, Frol Zapolsky
We construct an embedding of the full braid group on strands , , into the contact mapping class group of the contactization of the -Mil…
The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory
Frol Zapolsky
The purpose of this paper is to extend the construction of the PSS-type isomorphism between the Floer homology and the quantum homology of a monotone Lagrangian submanifold of…
Spectral invariants for monotone Lagrangians
Rémi Leclercq, Frol Zapolsky
Since spectral invariants were introduced in cotangent bundles via generating functions by Viterbo in the seminal paper "Symplectic topology as the geometry of generating functions…
Quasi-morphisms on contactomorphism groups and contact rigidity
Matthew Strom Borman, Frol Zapolsky
We build homogeneous quasi-morphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Gi…
Geometric structures on contactomorphism groups and contact rigidity in jet spaces
Frol Zapolsky
For a closed connected manifold N, we establish the existence of geometric structures on various subgroups of the contactomorphism group of the standard contact jet space J^1N, as…
On the Lagrangian Hofer geometry in symplectically aspherical manifolds
Frol Zapolsky
We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, dependi…
Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization
Alexandra Monzner, Nicolas Vichery, Frol Zapolsky
For a closed connected manifold N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T^*N, and a family of functions on the space of smooth func…
Quasi-morphisms on cotangent bundles and symplectic homogenization
Alexandra Monzner, Nicolas Vichery, Frol Zapolsky
For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the s…
A comparison of symplectic homogenization and Calabi quasi-states
Alexandra Monzner, Frol Zapolsky
We compare two functionals defined on the space of continuous functions with compact support in an open neighborhood of the zero section of the cotangent bundle of a torus. One com…
On almost Poisson commutativity in dimension two
Frol Zapolsky
Consider the following question: given two functions on a symplectic manifold whose Poisson bracket is small, is it possible to approximate them in the norm by commuting func…
Quasi-states and the Poisson bracket on surfaces
Frol Zapolsky
We present a convexity-type result concerning simple quasi-states on closed manifolds. As a corollary, an inequality emerges which relates the Poisson bracket and the measure of no…
Quasi-morphisms and the Poisson bracket
Michael Entov, Leonid Polterovich, Frol Zapolsky
For a class of symplectic manifolds, we introduce a functional which assigns a real number to any pair of continuous functions on the manifold. This functional has a number of inte…