Related papers: Higher $P$-symmetric Ekeland-Hofer capacities

In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product)…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

We consider the Tarski--Bang problem about covering of convex bodies by planks. The results of this kind give a lower bound on the sum of widths of planks (regions between a pair of parallel hyperplanes) covering a given convex body.…

For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations…

This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…

We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg…

We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an…

In this article we study two classical potential-theoretic problems in convex geometry corresponding to a nonlinear capacity, $\mbox{Cap}_{\mathcal{A}}$, where $\mathcal{A}$-capacity is associated with a nonlinear elliptic PDE whose…

In this note we show that one open four dimensional ellipsoid embeds symplectically into another if and only the ECH capacities of the first are no larger than those of the second. This proves a conjecture due to Hofer. The argument uses…

We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…

Let $k$ be an algebraically closed field, $l\neq\operatorname{char} k$ a prime number, and $X$ a quasi-projective scheme over $k$. We show that the \'etale homotopy type of the $d$th symmetric power of $X$ is $\mathbb Z/l$-homologically…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

We provide a lower bound for the embedding capacity of higher-dimensional symplectic ellipsoids, formulated in terms of the Lagrangian capacity of ellipsoids. Our approach relies on examining the Borman--Sheridan class of a Weinstein…

This paper continues to carry out a foundational study of Banyaga topologies of a closed symplectic manifold [3]. Our intension in writing this paper is to provide several symplectic analogues of some results found in the study of…

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK\cap P are also discussed, where gK is a…

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…

We introduce the symplectic holomorphic density property and the Hamiltonian holomorphic density property together with the corresponding version of Anders\'en-Lempert theory. We establish these properties for the Calogero-Moser space…

In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-K\"ahler manifolds $(X,J,g,\omega)$ with $J$ $\mathcal{C}^\infty$-pure and full the space of de Rham…

We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have…