Related papers: Existence of symplectic structures on torus bundle…

We construct symplectic structures on roughly half of all equal rank biquotients of the form $G//T$, where $G$ is a compact simple Lie group and $T$ a torus, and investigate Hamiltonian Lie group actions on them. For the Eschenburg flag,…

In this paper, we study the well-know $g$-conjecture for rational homology spheres in a topological way. To do this, we construct a class of topological spaces with torus actions, which can be viewed as topological generalizations of toric…

This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the…

Branched covers of orbit cylinders are the basic examples of holomorphic curves studied in symplectic field theory. Since all curves with Fredholm index one can never be regular for any choice of cylindrical almost complex structure, we…

In this note we investigate the simplicial volume of fiber bundles with connected structure group. We are able to show that if the structure group is either compact or a Lie group, or if the fiber is aspherical that the simplicial volume of…

We show that, given a closed integral symplectic manifold $(\Sigma, \omega)$ of dimension $2n \geq 4$, for every integer $k>\int_{\Sigma}\omega^{n}$, the Boothby-Wang bundle over $(\Sigma, k\omega)$ carries no Stein fillable contact…

We study line bundles on toric DM stacks $\mathbb{P}_{\mathbf{\Sigma}}$ of dimension two. We give a combinatorial criterion of when infinitely many line bundles on $\mathbb{P}_{\mathbf{\Sigma}}$ have trivial cohomology. We further discuss…

An interesting question in symplectic topology, which was posed by C. H. Taubes, concerns the topology of closed (i.e. compact and without boundary) connected oriented three dimensional manifolds whose product with a circle admits a…

We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use…

A symplectic bundle over an algebraic curve has a natural invariant $\sLag$ determined by the maximal degree of its Lagrangian subbundles. This can be viewed as a generalization of the classical Segre invariants of a vector bundle. We give…

Consider a fiber bundle in which the total space, the base space and the fiber are all symplectic manifolds. We study the relations between the quantization of these spaces. In particular, we discuss the geometric quantization of a vector…

We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for $K3$ surfaces by constructing big line bundles of low degree on certain moduli…

We prove that an element of the symplectic Steinberg group is trivial if and only if its image under any maximal localisation homomorphism is trivial.

This paper consists of two parts. In the first part, we use symplectic homology to distinguish the contact structures on the Brieskorn manifolds $\Sigma(2l,2,2,2)$, which contact homology cannot distinguish. This answers a question from…

Projective structures on topological surfaces support the structure of 2d CFTs with a degree of technical simplification. We propose a complex analytic space $\mathcal{P}_g$ biholomorphic to $T^*_{(1,0)} \mathcal{M}_g$ as a candidate moduli…

In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $\sigma$ on the smooth locus, and for which every finite…

Let $X$ be any compact connected Riemann surface of genus $g \geq 3$. For any $r\geq 2$, let $M_X$ denote the moduli space of holomorphic $SL(r,C)$-connections over $X$. It is known that the biholomorphism class of the complex variety $M_X$…

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,…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearly independent holomorphic sections.…