Developments in Symplectic Topology

Characteristic Classes in Symplectic Topology

SYMPLECTIC TOPOLOGY OF b-SYMPLECTIC MANIFOLDS

A Poisson manifold (M2n, π) is b-symplectic if ∧n π is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to b-symplectic manifolds. The main results provide constructions of: b-symplectic submanifolds à la Donaldson, b-symplectic structures on open manifolds by Gromov’s h-principle, and of b-symplectic manifolds with ...

Symplectic Topology and Capacities

I am going to talk about symplectic topology, a field that has seen a remarkable development in the past 15 years. Let’s begin with what was classically known – which was rather little. We start with a symplectic form ω, that is, a closed 2-form which is nondegenerate. This last condition means that ω is defined on an even dimensional manifold M and that its wedge with itself n times is a top d...

On Some Examples in Symplectic Topology

Article is devoted to the Examples 2 and 3 of the symplectic solvable Lie groups R with some special cohomological properties, which have been constructed by Benson and Gordon. But they are not succeeded in constructing corresponding compact forms for symplectic structures on these Lie groups. Recently A.Tralle proved that there is no compact form in the Example 3. But his proof is rather compl...

Four dimensions from two in symplectic topology

This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these diagrams. The paper offers a purely topological approach to toric manifolds as well as methods for visualizing other manifolds, including the K3 surface, and...