Related papers: On Stein rational balls smoothly but not symplecti…

We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as…

Let C be a smooth projective curve of genus at least 2 over a field k. Given a line bundle L on C, we consider the moduli stack of rank 2n vector bundles E on C endowed with a nowhere degenerate symplectic form $b: E \otimes E \to L$ up to…

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth…

In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.

A recent result of Chepoi, Estellon and Vaxes [DCG '07] states that any planar graph of diameter at most 2R can be covered by a constant number of balls of size R; put another way, there are a constant-sized subset of vertices within which…

Let X be a minimal surface of general type with positive geometric genus ($b_+ > 1$) and let $K^2$ be the square of its canonical class. Building on work of Khodorovskiy and Rana, we prove that if X develops a Wahl singularity of length…

The Lagrangian skeleton of the rational homology ball $B_{p,q}$, for $0<q<p$ coprime integers, is an immersed but not embedded Lagrangian, called a $(p,q)$-pinwheel. We show that any two embeddings of Lagrangian $(p,q)$-pinwheels in…

We show that, in certain circumstances, a Boolean ample monoid may be fully embedded into a Boolean inverse monoid in a way that generalizes how right reversible cancellative monoids may be embedded into groups. We use groupoids of…

Let M be the moduli space of stable bundles of rank 2 and with fixed determinant \mathcal{L} of degree d on a smooth projective curve C of genus g>= 2. When g=3 and d is even, we prove, for any point [W]\in M, there is a minimal rational…

We study stable rationality of conic bundles $X$ over $\mathbb{P}^1$ defined over non-closed field $k$ via the cohomology of the Galois group of finite field extension $k'/k$ with action on the geometric Picard lattice of $X$.

We prove that an infinite family of virtually overtwisted tight contact structures discovered by Honda on certain circle bundles over surfaces admit no symplectic semi-fillings. The argument uses results of Mrowka, Ozsvath and Yu on the…

We construct smooth 4-manifolds homeomorphic but not diffeomorphic to $CP^2#k\bar{CP^2},k \in {6,7,8,9}$, using the technique of rational blow-down along Wahl type plumbing trees of spheres.

We study harmonic bundles with an additional structure called symplectic structure. We study them for the case of the base manifold is compact and non-compact. For the compact case, we show that a harmonic bundle with a symplectic structure…

A unified summary is given of the existence theory of Stein manifolds in all dimensions, based on published and pending literature. Eliashberg's characterization of manifolds admitting Stein structures requires an extra delicate hypothesis…

We discuss the symplectic topology of the Stein manifolds obtained by plumbing two 3-dimensional spheres along a circle. These spaces are related, at a derived level and working in a characteristic determined by the specific geometry, to…

Consider a symplectic embedding of a disjoint union of domains into a symplectic manifold $M$. Such an embedding is called Kahler-type, or respectively tame, if it is holomorphic with respect to some (not a priori fixed, Kahler-type)…

The smooth rational homology cobordism group of rational homology three spheres, T, contains subgroups T_p generated by 3-manifolds with first homology p-torsion, where p is a prime. Rochlin's theorem and gauge theoretic methods show that…

Recently, Tsai-Tseng-Yau constructed new invariants of symplectic manifolds: a sequence of Aoo-algebras built of differential forms on the symplectic manifold. We show that these symplectic Aoo-algebras have a simple topological…

We construct explicit maximal symplectic packings of minimal rational and ruled symplectic 4-manifolds by few balls in a very simple way.