Related papers: Critical symplectic connections on surfaces
A study of symplectic actions of a finite group $G$ on smooth 4-manifolds is initiated. The central new idea is the use of $G$-equivariant Seiberg-Witten-Taubes theory in studying the structure of the fixed-point set of these symmetries.…
We study the relation between the symplectomorphism group Symp M of a closed connected symplectic manifold M and the symplectomorphism and diffeomorphism groups Symp \TM and Diff \TM of its one point blow up \TM. There are three main…
The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critical points of a smooth function on the manifold. It is well…
The group $Ham(M,\omega)$ of all Hamiltonian diffeomorphisms of a symplectic manifold $(M,\omega)$ plays a central role in symplectic geometry. This group is endowed with the Hofer metric. In this paper we study two aspects of the geometry…
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…
A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then…
We discuss $C^0$-continuous homogeneous quasi-morphisms on the identity component of the group of compactly supported symplectomorphisms of a symplectic manifold. Such quasi-morphisms extend to the $C^0$-closure of this group inside the…
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…
Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group…
In the early $1980$s a landmark result was obtained by Atiyah and independently Guillemin and Sternberg: the image of the momentum map for a torus action on a compact symplectic manifold is a convex polyhedron. Atiyah's proof makes use of…
The critical behaviour of semi-infinite $d$-dimensional systems with short-range interactions and an O(n) invariant Hamiltonian is investigated at an $m$-axial Lifshitz point with an isotropic wave-vector instability in an $m$-dimensional…
This paper investigates ways to enlarge the Hamiltonian subgroup Ham of the symplectomorphism group Symp(M) of the symplectic manifold (M, \omega) to a group that both intersects every connected component of Symp(M) and characterizes…
We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed.…
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed…
We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist…
By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-K\"ahler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a…
A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…
In this paper, we prove that if the area functional of a surface $\Sigma^2$ in a symplectic manifold $(M^{2n},\bar{\omega})$ has a critical point or has a compatible stable point in the same cohomology class, then it must be…
We show that contact reductions can be described in terms of symplectic reductions in the traditional Marsden-Weinstein-Meyer as well as the constant rank picture. The point is that we view contact structures as particular (homogeneous)…
We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…