13 citations · 22 across the 6 of their papers we have counts for
6 papers
Reeb graph and quasi-states on the two-dimensional torus
Frol Zapolsky
This note deals with quasi-states on the two-dimensional torus. Quasi-states are certain quasi-linear functionals (introduced by Aarnes) on the space of continuous functions. Grubb…
Isotopy-invariant topological measures on closed orientable surfaces of higher genus
Frol Zapolsky
Given a closed orientable surface (Σ) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (Σ) and…
Functoriality in Morse theory on closed manifolds
Avraham Aizenbud, Frol Zapolsky
We develop functoriality for Morse theory, namely, to a pair of Morse-Smale systems and a generic smooth map between the underlying manifolds we associate a chain map between the c…
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…
An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics
Michael Entov, Leonid Polterovich, Frol Zapolsky
We report on an "anti-Gleason" phenomenon in classical mechanics: in contrast with the quantum case, the algebra of classical observables can carry a non-linear quasi-state, a mono…
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…