Related papers: Extensions of the coeffective complex

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators…

This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics, that provides a very short survey of derived symplectic geometry. Derived symplectic geometry studies symplectic structures on derived stacks.…

In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts…

The analogies between symplectic and orthogonal groups, regarded as symmetries of real bilinear forms, are manifest in their (metaplectic and spin) projective representations. In finite dimensions, those are true representations of doubly…

We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in $W^{1, 1} (M, N)$, where $M$ is Riemannian manifold with compact boundary $\partial M$ and $N$ is a complete Riemannian manifold. The…

We construct a smooth codimension-one foliation on the five-sphere in which every leaf is a symplectic four-manifold and such that the symplectic structure varies smoothly. Our construction implies the existence of a complete regular…

Symmetric powers of quasi-projective schemes can be extended, in terms of left Kan extensions, to geometric symmetric powers of motivic spaces. In this paper, we study geometric symmetric powers and compare with various symmetric powers in…

We explain a general construction through which concave elliptic operators on complex manifolds give rise to concave functions on cohomology. In particular, this leads to generalized versions of the Khovanskii-Teissier inequalities.

In this paper we deal with symplectic Lie algebras. All symplectic structures are determined for dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described…

We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…

We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…

We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.

We generalise the theories of cosymplectic, contact, and cocontact manifolds to the infinite-dimensional setting and calculate model examples of time-dependent and dissipative Hamiltonian systems.

The study of algebraic properties of groups of transformations of a manifold gives rise to an interplay between different areas of mathemathics such as topology, geometry, and dynamical systems. Especially, in this paper, we point out some…

The cobordism ring of symplectic manifolds defined by V.L. Ginzburg is shown to be isomorphic to the Pontrjagin ring of complex-oriented manifolds with free circle actions. This suggests an interpretation of the formal group law of complex…

We consider character expansion of tau functions and multiple integrals in characters of orhtogonal and symplectic groups. In particular we consider character expansions of integrals over orthogonal and over symplectic matrices.

We present an alternative proof of the Coisotropic Embedding Theorem in which the geometric choice of a connection is recast as the algebraic choice of an embedding into the cotangent bundle. The symplectic thickening is then identified as…

We study the integrability of a (almost) complex structure calibrated by a symplectic form. We find new sufficent conditions.