Related papers: Orbital cohomology and Kahler rigidity

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

We prove that every open $\sigma$-locally Polish groupoid $G$ is Borel equivalent to the groupoid of models on the Urysohn sphere $\mathbb{U}$ of an $\mathcal{L}_{\omega_1\omega}$-sentence in continuous logic. In particular, the orbit…

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

We construct the cohomology groups with compact support of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients. We construct the cuspidal cohomology groups and prove that they are $\mathbb Z_{\ell}$-modules of finite type. We prove that…

We show that for any Polish group $G$ and any countable normal subgroup $\Gamma\triangleleft G$, the coset equivalence relation $G/\Gamma$ is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any…

We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume that $\Sigma<\Gamma$ are countable groups such that $g\Sigma g^{-1}\cap \Sigma$ is…

Let $G$ be a group acting continuously on a space $X$ and let $X/G$ be its orbit space. Determining the topological or cohomological type of the orbit space $X/G$ is a classical problem in the theory of transformation groups. In this paper,…

Let $G$ be a connected reductive algebraic group and $B$ be a Borel subgroup defined over an algebraically closed field of characteristic $p>0$. In this paper, the authors study the existence of generic $G$-cohomology and its stability with…

Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…

Let F be an arbitrary family of subgroups of a group G and let Orb be the associated orbit category. We investigate interpretations of low dimensional F-Bredon cohomology of G in terms of abelian extensions of Orb. Specializing to fixed…

A result due to M. Gromov states that any two finitely generated groups {\Gamma} and {\Lambda} are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions…

Recent work of Chen He has determined through GKM methods the Borel equivariant cohomology with rational coefficients of the isotropy action on a real Grassmannian and an real oriented Grassmannian through GKM methods. In this expository…

Given a Polish group $G$, let $E(G)$ be the right coset equivalence relation $G^\omega/c(G)$, where $c(G)$ is the group of all convergent sequences in $G$. The connected component of the identity of a Polish group $G$ is denoted by $G_0$.…

Let $G$ be a group of permutations of a denumerable set $E$. The profile of $G$ is the function $\phi_G$ which counts, for each $n$, the (possibly infinite) number $\phi_G(n)$ of orbits of $G$ acting on the $n$-subsets of $E$. Counting…

A topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of the socalled Bergman property in the context…

Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert…

Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory tells that the ring of invariants A^G=H^0(G,A) is…

We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by…

The paper is devoted to a study of generic representations (homomorphisms) of discrete countable groups $\Gamma$ in Polish groups $G$, i.e. those elements in the Polish space $\mathrm{Rep}(\Gamma,G)$ of all representations of $\Gamma$ in…

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…