Related papers: Maps with symplectic graphs

We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.

We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for compact effective group actions on spheres and provide…

Given a closed surface S of genus at least 2, we compare the symplectic structure of Taubes' moduli space of minimal hyperbolic germs with the Goldman symplectic structure on the character variety X(S, PSL(2,C)) and the affine cotangent…

We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-dimensional linear space or a nonstandard symplectic…

We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be non-exact and non-compactly supported, provided one uses the correct local system of…

Let M be a closed symplectic manifold with a compatible almost complex structure J. We prove that for a point p in M and E>0, if v is a non-constant J-holomorphic curve with symplectic area smaller than E, then the number of the pre-images…

The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…

We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. We show that the symplectomorphism type is also invariant for deformations which…

Given a symplectomorphism f of a symplectic manifold X, one can form the `symplectic mapping cylinder' $X_f = (X \times R \times S^1)/Z$ where the Z action is generated by $(x,s,t)\mapsto (f(x),s+1,t)$. In this paper we compute the Gromov…

This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…

The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of such a theorem in the more general multisymplectic framework…

We study homotopy groups of spaces of long links in Euclidean space of codimension at least three. With multiple components, they admit split injections from homotopy groups of spheres. We show that, up to knotting, these account for all…

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…

We consider, for a finite graph $G$, when the surjective map $\mathrm{Conf}_{n+1}(G) \rightarrow \mathrm{Conf}_n(G)$ of configuration spaces admits a section. We study when the answer depends only on the homotopy type of $G$, and give a…

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.…

Motivated by the path integral analysis of boundary conditions in a 3-dimensional topological sigma-model, we suggest a definition of the 2-category associated with a holomorphic symplectic manifold X and study its properties. The simplest…

Parametrized topological complexity is a homotopy invariant that represents the degree of instability of motion planning problem that involves external constraints. We consider the parametrized topological complexity in the case of…

In this paper we find connection between the Hofer's metric of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold, with an integral symplectic form, and the geometry, defined in a paper by Eliashberg and Polterovich,…

A symplectic semitoric manifold is a symplectic $4$-manifold endowed with a Hamiltonian $(S^1 \times \mathbb{R})$-action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic…

A smooth map between manifolds is said to be \emph{image simple} if its restriction to its singular point set is a topological embedding. We study the parity of the number of connected components of the singular point set for image simple…