Related papers: Comparison of two equivariant $\eta$-forms

Let $\mathcal{G}$ be an algebraic quantum group and $\mathcal{U}$ a compact quantum subgroup. Given a left $\hat{\mathcal{U}}$-module algebra A with unit, we can endow $A\otimes\mathcal{G}$ with a structure of a right…

We show that there is an one-to-one correspondence between resolutions (equivariant w.r.t. a Lie groupoid action) of a singular subset of a manifold, and substacks (of a certain type) of the differential stack associated to the Lie groupoid…

We prove that if two associative deformations (parameterized by the same complete local ring) are derived Morita equivalent, then they are Morita equivalent (in the classical sense).

In this paper, we give proofs of the family index formula and the equivariant family index formula by the Greiner's approach to heat kernel asymptotics. We compute equivariant family JLO characters. We also define the equivariant eta form…

Let $V, W$ be finite-dimensional orthogonal representations of a finite group $G$. The equivariant degree with values in the Burnside ring of $G$ has been studied extensively by many authors. We present a short proof of the degree product…

The problem of equivariant rigidity is the $\Gamma$-homeomorphism classification of $\Gamma$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $\Gamma$. In other words, this is the…

We apply the equivariant Burnside group formalism to distinguish linear actions of finite groups, up to equivariant birationality. Our approach is based on De Concini-Procesi models of subspace arrangements.

We present a new proof, as well as a ${\bf C/Q}$ extension, of the Riemann-Roch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of $\eta$-invariants…

We investigate an equivariant generalization of Morse theory for a general class of integrable models. In particular, we derive equivariant versions of the classical Poincar\'e-Hopf and Gauss-Bonnet-Chern theorems and present the…

In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid…

Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization…

We introduce the etale framework to study Igusa zeta functions in several variables, generalizing the machinery of vanishing cycles in the univariate case. We define the etale Alexander modules, associated to a morphism of varieties F from…

We study integrals of the form $\int_{\Omega}f\left( d\omega\right)$, where $1\leq k\leq n$, $f:\Lambda^{k}\rightarrow\mathbb{R}$ is continuous and $\omega$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity,…

Let G and K be groupoids. We present the notion of a (G_{\alpha},K_{\beta})-set and we prove a duality theorem in this context, which extends the duality theorem for graded algebras by groups. For A a unital G-graded algebra and X a finite…

In this paper we study uniform quasiconformal groups of Carnot-by-Carnot groups. We show that they can be conjugated into conformal groups provided the induced action on the space of distinct pairs is cocompact. Following the approach of…

The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of…

Let G be a compact Lie group. Let M be a smooth G-manifold and V --> M be an oriented G-equivariant vector bundle. One defines the spaces of equivariant forms with generalized coefficients on V and M. An equivariant Thom form $\theta$ on V…

An explicit identity of sums of powers of complex functions presented via this a closed-form formula of Riemann zeta function produced at any given non-zero complex numbers. The closed-form formula showed us Riemann zeta function has no…

The class of $\eta$-quasiconvex functions was introduced in 2016. Here we establish novel inequalities of Ostrowski type for functions whose second derivative, in absolute value raised to the power $q\geq 1$, is $\eta$-quasiconvex. Several…

Let M be a Hamiltonian T space with a proper moment map, bounded below in some component. In this setting, we give a combinatorial description of the T-equivariant cohomology of M, extending results of Goresky, Kottwitz and MacPherson and…