相关论文: Differential forms canonically associated to even-…

For odd dimensional Poincar\'e-Einstein manifolds $(X^{n+1},g)$, we study the set of harmonic $k$-forms (for $k<\ndemi$) which are $C^m$ (with $m\in\nn$) on the conformal compactification $\bar{X}$ of $X$. This is infinite dimensional for…

Given a mechanical system $(M, \mathcal{F}(M))$, where $M$ is a Poisson manifold and $\mathcal{F}(M)$ the algebra of regular functions on $M$, it is important to be able to quantize it, in order to obtain more precise results than through…

We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered…

It is known that irreducible noncommutative differential structures over $\Bbb F_p[x]$ are classified by irreducible monics $m$. We show that the cohomology $H_{\rm dR}^0(\Bbb F_p[x]; m)=\Bbb F_p[g_d]$ if and only if ${\rm Tr}(m)\ne 0$,…

Starting from a Riemannian conformal structure on a manifold M, we provide a method to construct a family of Lorentzian manifolds. The construction relies on the choice of a metric in the conformal class and a smooth 1-parameter family of…

We find the local form of all non-closed Lorentzian Weyl manifolds $(M,c,\nabla)$ with recurrent curvature tensor.If the dimension of the manifold is greater than 3, then the conformal structure is flat, and the recurrent Weyl structure is…

We construct open-closed maps on various versions of Hochschild and cyclic homology of the Fukaya $A_\infty$ algebra of a Lagrangian submanifold modeled on differential forms. The $A_\infty$ algebra may be curved. Properties analogous to…

We study the compactly supported rational cohomology of configuration spaces of points on wedges of spheres, equipped with natural actions of the symmetric group and the group $Out(F_g)$ of outer automorphisms of the free group. These…

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…

Universal Deformation Formulas (UDFs) for the deformation of associative algebras play a key role in deformation quantization. Here we present examples for certain classes of infinitesimals. A basic representable 2-cocycle $F$ of an…

Starting from simple and necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for instance, for the stable homotopy categories of…

Based on work of R. Lazarsfeld and M. Popa, we use the derivative complex associated to the bundle of the holomorphic p-forms to provide inequalities for all the Hodge numbers of a special class of irregular compact Kaehler manifolds. For…

Finite difference methods (FDMs) are widely used for solving partial differential equations (PDEs) due to their relatively simple implementation. However, they face significant challenges when applied to non-rectangular domains and in…

Conformal geometry is studied using the unfolded formulation \`a la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of…

We prove that two quasi-isomorphic simply connected differential graded associative Frobenius algebras have isomorphic Goresky-Hingston algebras on their reduced Hochschild homology. Our proof is based on relating the Goresky-Hingston…

Let $f\colon M^{2n}\to\mathbb{R}^{2n+\ell}$, $n \geq 5$, denote a conformal immersion into Euclidean space with codimension $\ell$ of a Kaehler manifold of complex dimension $n$ and free of flat points. For codimensions $\ell=1,2$ we show…

A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…

We construct a monomorphism of the De Rham complex of scalar multivalued meromorphic forms on the projective line, holomorphic on the complement to a finite set of points, to the chain complex of the Lie algebra of $sl_2$-valued algebraic…

Conformally compactified (3+1)-dimensional Minkowski spacetime may be identified with the projective light cone in (4+2)-dimensional spacetime. In the latter spacetime the special conformal group acts via rotations and boosts, and conformal…

Differential forms on the Fr\'echet manifold F(S,M) of smooth functions on a compact k-dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the…