Related papers: Four dimensions from two in symplectic topology

In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.

Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here we showcase…

We introduce a symplectic surgery in six dimensions which collapses Lagrangian three-spheres and replaces them by symplectic two-spheres. Under mirror symmetry it corresponds to an operation on complex 3-folds studied by Clemens, Friedman…

In this paper we define a new category of almost complex riemannian 4- manifolds and discuss some basic properties of such pseudo symplectic manifolds. Some motivation based on the Seiberg - Witten theory is imposed.

We describe a very nice argument, which we learned from Sue Tolman, that the dimension of the quantization space of a toric manifold, using a Kaehler polarization, is given by the number of integer lattice points in the moment polytope.

In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional…

A presymplectic structure on odd dimensional manifold is given by a closed 2-form which is nondegenerate, i.e., of maximal rank. We investigate geometry of presymplectic manifolds. Some basic theorems analogous to those in symplectic and…

Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in six dimensions, and we use this correspondence to interpret symplectic fibrations between these orbits, and to analyse moment polytopes associated to the standard…

This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality.…

In this article we study covering spaces of symplectic toric orbifolds and symplectic toric orbifold bundles. In particular, we show that all symplectic toric orbifold coverings are quotients of some symplectic toric orbifold by a finite…

The quantum homology of the monotone complex quadric surface splits into the sum of two fields. We outline a proof of the following statement: The unities of these fields give rise to distinct symplectic quasi-states defined by asymptotic…

When geometric quantization is applied to a manifold using a real polarization which is "nice enough", a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld leaves. Subsequently,…

We will survey some aspects of the smooth topology, algebraic geometry, symplectic geometry and contact geometry of anti-canonical pairs in complex dimension two.

We give a characterization of irreducible symplectic fourfolds which are given as Hilbert scheme of points on a K3 surface.

A manifold obtained by k simultaneous symplectic blow-ups of CP^2 of equal sizes epsilon (where the size of CP^1 in CP^2 is one) admits an effective two-dimensional torus action if k <= 3. We show that it does not admit such an action if k…

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

The contribution emphasizes the geometric modeling point of view on Minkowski point set operations. In this paper, the Minkowski product is specified as the quaternionic product. Selected point sets are visualized using double orthogonal…

Following Thurston's geometrisation picture in dimension three, we study geometric manifolds in a more general setting in arbitrary dimensions, with respect to the following problems: (i) The existence of maps of non-zero degree (domination…

We review, from a didactic point of view, the definition of a toric section and the different shapes it can take. We'll then discuss some properties of this curve, investigate its analogies and differences with the most renowned conic…

We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…