Related papers: Symplectic capacities from Hamiltonian circle acti…

We improve the estimates for the Ekeland--Hofer--Zehnder capacity of convex bodies by Gluskin and Ostrover. In the course of our argument we show that a closed characteristic of minimal action on the boundary of a centrally symmetric convex…

We consider two disjoint and homotopic non-contractible embedded loops on a Riemann surface and prove the existence of a non-contractible orbit for a Hamiltonian function on the surface whenever it is sufficiently large on one of the loops…

Using a "Hodge decomposition" of symplectic isotopies on a compact symplectic manifold $(M,\omega)$, we construct a norm on the identity component in the group of all symplectic diffeomorphisms of $(M,\omega)$ whose restriction to the group…

The special structures that arise in symplectic topology (particularly Gromov--Witten invariants and quantum homology) place as yet rather poorly understood restrictions on the topological properties of symplectomorphism groups. This…

We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using…

Motivated by recent works on Hamiltonian circle actions satisfying certain minimal conditions, in this paper, we consider Hamiltonian circle actions satisfying an almost minimal condition. More precisely, we consider a compact symplectic…

We find bounds for the Hofer-Zehnder capacity of coadjoint orbits of compact Lie groups with respect to the Kostant--Kirillov--Souriau symplectic form in terms of the combinatorics of their Bruhat graph. We show that our bounds are sharp…

We prove that any symplectic Fano $6$-manifold $M$ with a Hamiltonian $S^1$-action is simply connected and satisfies $c_1 c_2(M)=24$. This is done by showing that the fixed submanifold $M_{\min}\subseteq M$ on which the Hamiltonian attains…

Let $V$ be a bounded domain with smooth boundary in $\R^n$, and $D^*V$ denote its disc cotangent bundle. We compute symplectic homology of $D^*V$, in terms of relative homology of loop spaces on the closure of $V$. We use this result to…

The first author introduced a relative symplectic capacity $C$ for a symplectic manifold $(N,\omega_N)$ and its subset $X$ which measures the existence of non-contractible periodic trajectories of Hamiltonian isotopies on the product of $N$…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

We derive a complete asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions on arbitrary symplectic manifolds, characterizing the coefficients in the expansion as integrals over the symplectic strata of the…

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on…

Let $(M,\omega)$ be a compact symplectic manifold with a Hamiltonian GKM action of a compact torus. We formulate a positive condition on the space; this condition is satisfied if the underlying symplectic manifold is monotone. The main…

We give an explicit formula for the Gromov width for a class of symplectic toric manifolds constructed from simple graphs. As a corollary, we show a version of non-squeezing theorem with respect to the inclusion of connected graphs.

We prove the elementary but surprising fact that the Hofer distance between two closed subsets of a symplectic manifold can be expressed in terms of the restrictions of Hamiltonians to one of the subsets; this helps explain certain…

In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of…

In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…

Many of the existing results for closed Hamiltonian G-manifolds are based on the analysis of the corresponding Hamiltonian functions using Morse-Bott techniques. In general such methods fail for non-compact manifolds or for manifolds with…

We consider symplectic manifolds with Hamiltonian torus actions which are "almost but not quite completely integrable": the dimension of the torus is one less than half the dimension of the manifold. We provide a complete set of invariants…