Related papers: Symplectic real Bott manifolds

This short and fairly informal note is an attempt to explain how methods of homological algebra may be brought to bear on problems in symplectic geometry. We do this by looking at a familiar sample question, which is that of the topology of…

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact,…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski…

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves…

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and…

Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We…

A regular contact manifold is a manifold $M$ equipped with a globally defined contact form $\eta$ such that the topological space $M/\mathcal{R}$ of orbits (trajectories) of the Reeb vector field $\mathcal{R}$ of $\eta$ carries a smooth…

We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one surprising result:…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build…

A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a…

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…

We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of…

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…

In this note we prove that a positive multiple of each even-dimensional integral homology class of a compact symplectic manifold $(M^{2n}, \omega)$ can be represented as the difference of the fundamental classes of two symplectic…

The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex…

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…

We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously.…

In this note we compute the cohomology of the elliptic tangent bundle, a Lie algebroid used to describe singular symplectic forms arising from generalized complex geometry.