Related papers: The twisted cohomological equation over the partia…

We study hyperbolized versions of cohomological equations that appear with cocycles by isometries of the euclidean space. These (hyperbolized versions of) equations have a unique continuous solution. We concentrate in to know whether or not…

Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond…

We describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern-Weil homomorphism to the twisted equivariant cohomology. We clarify that in order to have…

The FDA algebras emerging from twisted tori compactifications of M-theory with fluxes are discussed within the general classification scheme provided by Sullivan's theorems and by Chevalley cohomology. It is shown that the generalized…

In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model on a complex orbifold X/G, where G is an isometry group of X. The objective is to furnish a purely physical interpretation of the…

Let M be a quasiprojective algebraic manifold with K_M=0 and G a finite automorphism group of M acting trivially on the canonical class K_M; for example, a subgroup G of SL(n,C) acting on C^n in the obvious way. We aim to study the quotient…

We calculate the cohomology spaces of the Hilbert schemes of points on surfaces with values in locally constant systems. For that purpose, we generalise I. Grojnoswki's and H. Nakajima's description of the ordinary cohomology in terms of a…

Let $G$ be a simply connected solvable Lie group with a lattice $\Gamma$ and $N$ the nilradical of $G$. For a complex valued representation $\rho: G\to GL(V_{\rho})$ such that the restriction $\rho_{|_{N}}$ is unipotent, as an advanced…

Let $\mathbb{F}_\ell$ be a finite field with $\ell$ elements and let $G = C_p \rtimes C_m$ be a faithful split metacyclic group. In this paper, we develop a complete theory for the twisted group algebra $\mathbb{F}_\ell^\alpha G$. Using the…

This is preprint HAL-00429963 (2009). I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves $\widehat{Z}_{I}\in H^{*}(\bar{\mathcal{M}}_{g,n})$ starting from the following data: an odd…

Standard results from non-abelian cohomology theory specialize to a theory of torsors and stacks for cosimplicial groupoids. The space of global sections of the stack completion of a cosimplicial groupoid $G$ is weakly equivalent to the…

We define a version of spectral invariant in the vortex Floer theory for a $G$-Hamiltonian manifold $M$. This defines potentially new (partial) symplectic quasi-morphism and quasi-states when $M//G$ is not semi-positive. We also establish a…

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant…

The tempered representations of a real reductive Lie group $G$ are naturally partitioned into series associated with conjugacy classes of Cartan subgroups $H$ of $G$. We define partial Dirac cohomology, apply it for geometric construction…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

In this paper, we present a unified framework for studying cohomology theories of various operators in the context of pseudoalgebras. The central tool in our approach is the notion of a quasi-twilled Lie pseudoalgebra. We introduce two…

We give a new proof of a Theorem of Vogan which classify the cohomological representations of a real semisimple Lie group $G$ which are isolated in the unitary dual of $G$. We investigate the same question in the automorphic dual, and…

Rollings of reductive homogeneous spaces are investigated. More precisely, for a reductive homogeneous space $G / H$ with reductive decomposition $\mathfrak{g} = \mathfrak{h} \oplus \mathfrak{m}$, we consider rollings of $\mathfrak{m}$ over…

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…

This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…