Related papers: Covariant and Equivariant Formality Theorems

Let $M$ denote a specific cubic fourfold that accommodates a group action by $\mathbb{Z}/3\mathbb{Z}$. Through utilization of derived Mckay correspondence, we present a new proof establishing the identification of the equivariant Kuznetsov…

A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ is commensurable to $H$. If $H$ is almost normal, there is a well-defined quotient space $G/H$. We show that if a group $G$ has type $F_{n+1}$ and contains an almost…

A general equivariant shape theory for arbitrary $G$-spaces in the case of a compact group $G$ is constructed by using the method of pseudometrics suggested by Yu. M. Smirnov as early as in 1985 at the fifth Tiraspol symposium on general…

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string…

Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is…

According to a statement by Pavel Etingof, in the special case of an affine variety $X$ with a faithful action by a finite group $G$, the sheaf of (twisted) Cherednik algebras $\mathcal{H}_{1, c, \psi, X, G}$ with formal parameters $c,…

We define and discuss G-formality for certain spaces endowed with an action by a compact Lie group. This concept is essentially formality of the Borel construction of the space in a category of commutative differential graded algebras over…

We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.

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…

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product…

In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket…

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one…

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The…

Given a bounded valence, bushy tree T, we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T'. This theorem has many applications: quasi-isometric rigidity…

Let $G$ be a complex simple Lie group, and $\mathfrak{g}$ its Lie algebra. It is well known that a finite-dimensional $G$-module $V$ carrying a nondegenerate invariant bilinear form gives rise to a Hamiltonian Poisson space with a quadratic…

In this work the equivariant signature of a manifold with proper action of a discrete group is defined as an invariant of equivariant bordisms. It is shown that the computation of this signature can be reduced to its computation on fixed…

We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal approaches within a unifying framework. First, we establish a…

The goal of this paper is to introduce the notion of $G$-Frobenius manifolds for any finite group $G$. This work is motivated by the fact that any $G$-Frobenius algebra yields an ordinary Frobenius algebra by taking its $G$-invariants. We…

In the mid 1980s, while working on establishing completion theorems for equivariant Algebraic K- Theory similar to the well-known Atiyah-Segal completion theorem for equivariant topological K-theory, the late Robert Thomason found the…

We prove that when Kontsevich's deformation quantization is applied on weight homogeneous Poisson structures, the operators in the $\ast-$ product formula are weight homogeneous. We then consider the linear Poisson case…