相关论文: Chiral de Rham Complex and Orbifolds
We describe the primitive middle-dimensional cohomology $\mathbb{H}$ of a compact simplicial toric complete intersection variety in terms of a twisted de Rham complex. Then this enables us to construct a concrete algorithm of formal flat…
Rickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to…
Hector, Mac\'{\i}as-Virg\'os, and Sanmart\'{\i}n-Carb\'on identified the complex of diffeological differential forms on the leaf space of a foliation with the complex of basic forms on the foliated manifold, yielding a canonical isomorphism…
We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some…
Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd…
Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates…
For the case of algebraic curves - compact Riemann surfaces - it is shown that de Rham cohomology group $H^{1}_{\mathrm{dR}}(X,\mathbb{C})$ of a genus $g$ Riemann surface $X$ has a natural structure of a symplectic vector space. Every…
Let $X$ be a smooth complex algebraic variety and let $\operatorname{Coh} (X)$ denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the deformation theory of $\operatorname{Coh}…
We establish a quantitative relationship between mixed de Rham classes and the geometric complexity of metric connections with totally skew torsion on product manifolds where both factors are compact oriented surfaces. For any…
We show that the cohomology group of the equivariant simplicial de Rham complex is isomorphic to the cohomology group of the classifying space of a semi-direct product group.
This note is a sequel to "Gerbes of chiral differential operators. II", math.AG/0003170. We study gerbes of chiral differential operators acting on the exterior algebra $\Lambda E$ of a vector bundle over a smooth algebraic variety $X$.…
If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X).…
When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting…
Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ between the orbifold cohomology of…
Twisting process for quantum linear spaces is defined. It consists in a particular kind of globally defined deformations on finitely generated algebras. Given a quantum space (A_1,A), a multiplicative cosimplicial quasicomplex C[A_1] in the…
We study a Lie algebra of formal vector fields $W_n$ with its application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. A relevant concept in the…
This paper provides a rigorous account on the geometry of forms on supermanifolds, with a focus on its algebraic-geometric aspects. First, we introduce the de Rham complex of differential forms and we compute its cohomology. We then discuss…
We introduce the notion of (homological) G-smoothness for a complex G-variety X, where G is a connected affine algebraic group. This is based on the notion of smoothness for dg algebras and uses a suitable enhancement of the G-equivariant…
The notion of twisted sectors play a crucial role in orbifold Gromov-Witten theory. We introduce the notion of dihedral twisted sectors in order to construct Lagrangian Floer theory on symplectic orbifolds and discuss related issues.
In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the…