Related papers: G-category versus orbifold category

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of…

In this paper configuration spaces of smooth manifolds are considered. The accent is made on actions of certain groups (mostly $p$-tori) on this spaces by permuting their points. For such spaces the cohomological index, the genus in the…

We construct a birational invariant for certain algebraic group actions. We use this invariant to classify linear representations of finite abelian groups up to birational equivalence, thus answering, in a special case, a question of E. B.…

For an arbitrary localic etale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is…

We introduce equivariant versions of uniform rationality: given an algebraic group G, a G-variety is called G-uniformly rational (resp. G-linearly uniformly rational) if every point has a G-invariant open neighborhood equivariantly…

Given a general finite group $G$, we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. For a certain class of transporter categories and their quotients, equipped with atomic topology, we…

We study the lower bounds and upper bounds for LS-category and equivariant LS-category. In particular we compute both invariants for torus manifolds. There are some examples to show the sharpness of conditions in the theorems. Moreover the…

Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in…

When a cyclic group G of prime order acts on a 4-manifold X, we prove a formula which relates the Seiberg-Witten invariants of X to those of X/G.

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the…

We introduce new Elmendorf constructions for equivariant categories and posets, and we prove that they are compatible with the classical topological one. Our constructions are more concrete than their model-categorical counterparts, and…

Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…

For $G$ a finite group, we prove in dimension 2 that there is a monoidal equivalence between the category of $G$-equivariant topological quantum field theories and the category of $G$-Frobenius algebras, this was proved by G. Moore and G.…

To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of…

We extend some of the results of Bondal-Orlov on the equivalence of derived categories to the case of orbifolds by using the category of coherent orbifold sheaves.

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

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…

Equivariant indices have previously been defined in cases where either the group or the orbit space in question is compact. In this paper, we develop an equivariant index without assuming the group or the orbit space to be compact. This…