Related papers: A de Rham theorem for symplectic quotients

On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We…

We show that Aomoto's $q$-deformation of de Rham cohomology arises as a natural cohomology theory for $\Lambda$-rings. Moreover, Scholze's $(q-1)$-adic completion of $q$-de Rham cohomology depends only on the Adams operations at each…

We introduce a Hilbert $A$-module structure on the higher oscillatory module, where $A$ denotes the $C^*$-algebra of bounded endomorphisms of the basic oscillatory module. We also define the notion of an exterior covariant derivative in an…

The idea of a space with smooth structure is a generalization of an idea of a manifold. K. T. Chen introduced such a space as a differentiable space in his study of a loop space to employ the idea of iterated path integrals…

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

We show that the Witten covariant phase space for p-branes with thickness in an arbitrary background is endowed of a symplectic potential, which although is not important to the dynamics of the system, plays a relevant role on the phase…

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack.…

If K is a commutative ring and A is a K-algebra, for any sequence $\sigma $ of positive integers there exists an higher order analogue dR($\sigma $) of the standard de Rham complex dR(1,...,1,...), which can also be defined starting from…

We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.

Let $(M,\omega)$ be a Hamiltonian $G$-space with a momentum map $F:M \to {\frak g}^*$. It is well-known that if $\alpha$ is a regular value of $F$ and $G$ acts freely and properly on the level set $F^{-1}(G\cdot \alpha)$, then the reduced…

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

In this note we consider a quantum reduction scheme in deformation quantization on symplectic manifolds proposed by Bordemann, Herbig and Waldmann based on BRST cohomology. We explicitly construct the induced map on equivalence classes of…

It is shown that the de Rham complex of a symplectic manifold $M$ satisfying the hard Lefschetz condition is formal. Moreover, it is shown that the differential Gerstenhaber-Batalin-Vilkoviski algebra associated to such a symplectic…

We exhibit a cocycle in the simplicial de Rham complex which represents the Euler class. As an application, we construct a Lie algebra cocycle on $L\mathfrak{so}(4)$.

In this paper we study whether symplectic toric manifolds are symplectically cohomologically rigid. Here we say that symplectic cohomological rigidity holds for some family of symplectic manifolds if the members of that family can be…

We introduce a version of the Cartier isomorphism for de Rham cohomology valid for associative, not necessarily commutative algebras over a field of positive characteristic. Using this, we imitate the well-known argument of P. Deligne and…

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…

Building on the recent computation of the cohomology rings of smooth toric varieties and partial quotients of moment-angle complexes, we investigate the naturality properties of the resulting isomorphism between the cohomology of such a…

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…