Related papers: Almost complex structure on finite points from bid…

The space of orientation-compatible almost complex structures on the six-dimensional sphere naturally contains a copy of seven-dimensional real projective space. We show that the inclusion induces an isomorphism on fundamental groups and…

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…

Many large, real-world complex networks have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological…

We study the space of closed anti-invariant forms on an almost complex manifold, possibly non compact. We construct families of (non integrable) almost complex structures on $\R^4$, such that the space of closed $J$-anti-invariant forms is…

We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.

We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…

It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite…

Considering an integer $d>0$, we show the existence of convex-cocompactrepresentations of surface groups into SO(4,1) admitting an embedded minimal map withcurvatures in $(-1,1)$ and whose associated hyperbolic 4-manifolds are disk bundles…

This article mainly aims to overview the recent efforts on developing algebraic geometry for an arbitrary compact almost complex manifold. We review the results obtained by the guiding philosophy that a statement for smooth maps between…

Let $X$ be an $(8k+i)$-dimensional pathwise connected $CW$-complex with $i=1$ or $2$ and $k\ge0$, $\xi$ be a real vector bundle over $X$. Suppose that $\xi$ admits a stable complex structure over the $8k$-skeleton of $X$. Then we get that…

We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…

Let $V$ be a finite set. Let $\mathcal{K}$ be a simplicial complex with its vertices in $V$. In this paper, we discuss some differential calculus on $V$. We construct some constrained homology groups of $\mathcal{K}$ by using the…

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial)…

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

We study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an $h$-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension $2n\geq 10$…