Related papers: On Equivariant Poincar\'e Duality, Gysin Morphisms…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…

Let $\pi$ be a group equipped with an action of a second group $G$ by automorphisms. We define the equivariant cohomological dimension ${\sf cd}_G(\pi)$, the equivariant geometric dimension ${\sf gd}_G(\pi)$, and the equivariant…

We geometrize the constructions of twisted Poisson modules introduced by Luo-Wang-Wu, and Poisson chain complexes with coefficients in Poisson modules defined in the algebraic setting to the geometric setting of Poisson manifolds. We then…

We study D-modules and related invariants on the space of 2 x 2 x n hypermatrices for n >= 3, which has finitely many orbits under the action of G = GL_2 x GL_2 x GL_n. We describe the category of coherent G-equivariant D-modules as the…

This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and…

We describe the algebra of invariants of the vacuum module associated with the affinization of the Lie superalgebra $\mathfrak{gl}(1|1)$. We give a formula for its Hilbert--Poincar\'{e} series in a fermionic (cancellation-free) form which…

Let G be a finite group acting on a finite dimensional real vector space V. We denote by P(V) the projective space associated to V. In this paper we compute in a very explicit way the rank of the equivariant complex K-theory of V and P(V),…

Let $G$ be the classical group, and let Hom$(\mathbb{Z}^m,G)$ denote the space of commuting $m$-tuples in $G$. First, we refine the formula for the Poincar\'e series of Hom$(\mathbb{Z}^m,G)$ due to Ramras and Stafa by assigning (signed)…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

We exhibit a Poisson module restoring a twisted Poincare duality between Poisson homology and cohomology for the polynomial algebra R=C[X_1,...,X_n] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This…

We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…

Greenlees and Sadofsky showed that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. We generalize their duality map and prove a K(n)-version…

In this paper we construct an equivariant Poincar\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended…

We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…

For a finite group G and a finite-dimensional G-module V, we prove a general result on the Poincar\'e series for the G-invariants in the tensor algebra T(V). We apply this result to the finite subgroups G of the 2-by-2 special unitary…

In this article we study the homology of spaces ${\rm Hom}(\mathbb{Z}^n,G)$ of ordered pairwise commuting $n$-tuples in a Lie group $G$. We give an explicit formula for the Poincare series of these spaces in terms of invariants of the Weyl…

We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…

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…

Poisson-Lie dualising the eta deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated lambda deformed model. In this paper we investigate…