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Symplectic Manifolds
In this chapter, we are going to see the definition of a symplectic manifold, several examples, and constructions of symplectic manifolds. We will...
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Symplectic Linear Algebra
A symplectic structure on a smooth manifold is defined by assigning a symplectic form to the tangent space at each point of the manifold, with...
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Remarks on Some Compact Symplectic Solvmanifolds
We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = Γ G of a simply-connected solvable Lie group G ...
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Symplectic Realizations of e(3)∗
Using the U(2, 2)-invariant symplectic structure of the Penrose twistor space we find full and complete E(3)-equivariant symplectic realizations of...
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Contact Symplectic Fibrations and Bundle Contact Structures
We consider a certain type of fiber bundles with odd dimensional connected contact base, exact symplectic fibers, and the structure group contained...
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On the existence of symplectic barriers
In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic...
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Injective and Tilting Resolutions and a Kazhdan-Lusztig Theory for the General Linear and Symplectic Group
Let k be an algebraically closed field of characteristic p > 0 and let G be a symplectic or general linear group over k . We consider induced modules...
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Contact and Symplectic Geometry
The even-dimensional moment-angle manifolds and the LVM-manifolds have the characteristic that, except for a few, well-determined cases, they do not...
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Normal Crossings Singularities for Symplectic Topology: Structures
Our previous papers introduce topological notions of normal crossings symplectic divisor and variety, show that they are equivalent, in a suitable...
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Products of two involutions in orthogonal and symplectic groups
An element of a group is called bireflectional when it is the product of two involutions of the group (i.e. elements of order 1 or 2). If an element...
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On a Symplectic Bigraded Toda Hierarchy
In this paper, we construct a symplectic bigraded Toda hierarchy which contains an symplectic deformation of the original Toda lattice hierarchy. In...
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Hamiltonian Symplectic Structures: An Introduction
The final chapter is devoted to formulating Hamiltonian Mechanics on symplectic manifolds and on bundles over symplectic manifolds. We will take the...
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The Arnold conjecture for singular symplectic manifolds
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of
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Symplectic Geometry and Hamiltonian Dynamics
The method of pseudoholomorphic curves was introduced by Gromov [Gro85]. The equation of Gromov’s pseudoholomorphic curves is conformally invariant....
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A Combinatorial Translation Principle and Diagram Combinatorics for the Symplectic Group
Let k be an algebraically closed field of characteristic p > 2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and...
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Branching Symplectic Monogenics Using a Mickelsson–Zhelobenko Algebra
In this paper we consider (polynomial) solution spaces for the symplectic Dirac operator (with a focus on 1-homogeneous solutions). This space forms...
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Asymptotically holomorphic theory for symplectic orbifolds
We extend Donaldson’s asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a compact symplectic orbifold such that...
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Extraspecial Groups, Symplectic Modules, and Hall’s Theorem
Here we look at extraspecial groups, their representations, and their connection to symplectic actions. We discuss in some detail Hall’s important...