Related papers: Non-extendability of complex structures

We study the existence and stability of holomorphic foliations in dimension greater than 4 under perturbations of the underlying almost complex structure. An example is given to show that, unlike in dimension 4, J-holomorphic foliations are…

While the standard construction of the S-matrix fails on Anti-de Sitter (AdS) spacetime, a generalized S-matrix makes sense, based on the hypercylinder geometry induced by the boundary of AdS. In contrast to quantum field theory in…

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many…

This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…

We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3-manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally…

We show that for $2\le d\le 4$, every finite geometric simplicial complex $\Delta$ in $\mathbb{R}^d$ with vertices on the moment curve can be extended to a triangulation $T$ of the cyclic polytope $C$ where $\Delta, T$ and $C$ all have the…

We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be…

Schwede proved very recently in arXiv:0901.1154 that in a quasiprojective scheme X with a fixed Frobenius splitting, there are only finitely many subschemes {Y} that are compatibly split. (A simpler proof has already since been given in…

The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. We discuss to what degree such…

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic…

We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical…

We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi--Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametrizing such deformations has…

We prove the existence of a deformation quantization for integrable Poisson structures on R^3 and give a generalization for a special class of three dimensional manifolds.

An automorphism $f$ of a closed orientable surface $\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \Sigma)$ with respect to some embedding $\Sigma \hookrightarrow S^3$. We prove…

The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable $\sigma$-models, solution-generating techniques in supergravity and…

We prove that any compact almost complex manifold $(M, J)$ of real dimension $2m$ admits a pseudo-holomorphic embedding in a Euclidean space of dimension $4m + 2$, endowed with a suitable non-standard almost complex structure. Moreover, we…

The generators $(J_{\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting point. An invertible nonlinear map involving, apart from q, a second arbitrary complex parameter h, defines a triplet $({\hat X},{\hat Y},{\hat H})$. The latter set…

This note is about the interplay between the almost-hermitian and Riemannian geometries of a manifold. These geometries can be seen to interact through curvature. The main result is an obstruction equation to the integrability of…

Let $A$ be a non-isotrivial almost ordinary abelian surface with possibly bad reductions over a global function field of odd characteristic $p$. Suppose $\Delta$ is an infinite set of positive integers, such that…