Related papers: Spencer manifolds

Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…

Let $(X,J)$ be a $4$-dimensional compact almost-complex manifold and let $g$ be a Hermitian metric on $(X,J)$. Denote by $\Delta_{\overline\partial}:=\overline\partial\overline\partial^*+\overline\partial^*\overline\partial$ the…

We give conditions on the Lee vector field of an almost Hermitian manifold such that any holomorphic map from this manifold into a (1,2)-symplectic manifold must satisfy the fourth-order condition of being biharmonic, hence generalizing the…

We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

We develop the theory of CW(A)-complexes, which generalizes the classical theory of CW-complexes, keeping the geometric intuition of J.H.C. Whitehead's original theory. We obtain this way generalizations of classical results, such as…

For any compact almost complex manifold $(M,J)$, the last two authors defined two subgroups $H_J^+(M)$, $H_J^-(M)$ of the degree 2 real de Rham cohomology group $H^2(M, \mathbb{R})$ in arXiv:0708.2520. These are the sets of cohomology…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. Relying on a basis of pseudodifferential…

This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show that the spectrum of $A$ decomposes,…

We show the intersection of a compact almost complex subvariety of dimension $4$ and a compact almost complex submanifold of codimension $2$ is a $J$-holomorphic curve. This is a generalization of positivity of intersections for…

After an elementary presentation of the relation between supersymmetric nonlinear sigma models and geometry, I focus on 2D and the target space geometry allowed when there is an extra supersymmetry. This leads to a brief introduction to…

Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves. It aims to systematically address…

In this paper we will show how to construct holomorphic L^{p}-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.

The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…

Let $(M,J)$ be a $2n$-dimensional almost complex manifold and let $x\in M$. We define the notion of almost complex blow-up of $(M,J)$ at $x$. We prove the existence of almost complex blow-ups at $x$ under suitable assumptions on the almost…

The paper reviews recent developments in the study of Alexander invariants of quasi-projective manifolds using methods of singularity theory. Several results in topology of the complements to singular plane curves and hypersurfaces in…

Reformulations of Donaldson's "tamed to compatible" question are obtained in terms of spaces of exact forms on a compact almost complex manifold $(M^{2n},J)$. In dimension 4, we show that $J$ admits a compatible symplectic form if and only…

We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the class of semi-positive manifolds with convex boundary. This…