Related papers: Hypercohomologies of truncated twisted holomorphic…

We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure…

The chiral de Rham complex of Malikov, Schechtman, and Vaintrob, is a sheaf of differential graded vertex algebras that exists on any smooth manifold $Z$, and contains the ordinary de Rham complex at weight zero. Given a closed 3-form $H$…

This is a slightly corrected version of the article published by Functional Analysis and its Applications in 1993. We define the quadratic duality for algebras with nonhomogeneous relations; the duality between the algebra of differential…

We discuss hypercomplex and hyperk\"ahler structures obtained from higher degree curves in complex spaces fibring over ${\mathbb{P}}^1$.

For a stratified pseudomanifold $X$, we have the de Rham Theorem $ \lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t} - \per{p}}{*}{X}, $ for a perversity $\per{p}$ verifying $\per{0} \leq \per{p} \leq \per{t}$, where $\per{t}$ denotes the top…

We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward…

Given a finite morphism $\varphi:Y\to X$ of quasi-smooth Berkovich curves over a complete, algebraically closed field $k$ of characteristic $0$, we prove a Riemann-Hurwitz formula relating their Euler-Poincar\'e characteristics (calculated…

We compute an analogue of Pascal's triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose $j$ ring homomorphisms into an algebraic closure from an \'etale extension of…

This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations

The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…

We prove a blow-up formula for Dolbeault cohomologies of compact complex manifolds by introducing relative Dolbeault cohomology. As corollaries, we present a uniform proof for bimeromorphic invariance of $(\bullet,0)$- and…

We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras $H$ and those for cocycle twists $H^{\sigma}$ of $H$. This implies an equivalence between modules…

This is the first of a series of papers on sheaf theory on smooth and topological stacks and its applications. The main result of the present paper is the characterization of the twisted (by a closed integral three-form) de Rham complex on…

The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},\omega)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the…

In this paper, we present a general construction to extract subcomplexes from two distinct complexes on filtered Riemannian manifolds. The first subcomplex computes the de Rham cohomology of the underlying manifold. On regular subRiemannian…

We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding…

A refined form of the `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established by the authors in the context of manifolds with corners; the…

These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.

We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived…

Let $X=\C^n$. In this paper we present an algorithm that computes the de Rham cohomology groups $H^i_{dR}(U,\C)$ where $U$ is the complement of an arbitrary Zariski-closed set $Y$ in $X$. Our algorithm is a merger of the algorithm given by…