Related papers: Ellipsoid embeddings and symplectic packing stabil…
We show how to reduce the problem of symplectically embedding one 4-dimensional rational ellipsoid into another to a problem of embedding disjoint unions of balls into appropriate blow ups of \C P^2. For example, the problem of embedding…
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…
The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…
The stable systolic category of a closed manifold M indicates the complexity in the sense of volume. This is a homotopy invariant, even though it is defined by some relations between homological volumes on M. We show an equality of the…
Rational homology ellipsoids are certain Liouville domains diffeomorphic to rational homology balls and having Lagrangian pin-wheels as their skeleta. From the point of view of almost toric fibrations, they are a natural generalisation of…
We prove a coisotropic intersection result and deduce the following: 1. Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. 2. A stable non-squeezing…
Let $X$ be a union of a sequence of symplectic manifolds of increasing dimension and let $M$ be a manifold with a closed $2$-form $\omega$. We use Tischler's elementary method for constructing symplectic embeddings in complex projective…
We exhibit an infinite family of rational homology balls which embed smoothly but not symplectically in the complex projective plane. We also obtain a new lattice embedding obstruction from Donaldson's diagonalisation theorem, and use this…
This paper is the last in a series of three papers which investigate pseudoholomorphic strips in the symplectisation of a three dimensional closed contact manifold with a mixed boundary condition. We will prove a compactness and an…
We show that the spherical capacity is discontinuous on a smooth family of ellipsoidal shells. Moreover, we prove that the shell capacity is discontinuous on a family of open sets with smooth connected boundaries.
In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…
We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.
Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…
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 prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…
The ECH capacities are a sequence of real numbers associated to any symplectic four-manifold, which are monotone with respect to symplectic embeddings. It is known that for a compact star-shaped domain in R^4, the ECH capacities…
A toric domain is a subset of $(\mathbb{C}^n,\omega_{\text{std}})$ which is invariant under the standard rotation action of $\mathbb{T}^n$ on $\mathbb{C}^n$. For a toric domain $U$ from a certain large class for which this action is not…
New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds…
We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result by Bertelson-Meigniez, states that in dimension at least 7…