Related papers: Extensions of Cantor minimal systems and dimension…
We show that every Grigorchuk group $G_\omega$ embeds in (the commutator subgroup of) the topological full group of a minimal subshift. In particular, the topological full group of a Cantor minimal system can have subgroups of intermediate…
The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…
Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to…
Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…
A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…
The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandle cohomology and certain group of automorphisms of an…
We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as…
We construct groups G that are virtually torsion-free and have virtual cohomological dimension strictly less than the minimal dimension for any model for the classifying space for proper actions of G. They are the first examples that have…
The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A…
This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson…
We give an explicit characterization for group extensions that correspond to elements of the symmetric cohomology $HS^2(G,A)$. We also give conditions for the map $HS^n(G,A)\to H^n(G,A)$ to be injective.
We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable…
Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely generated dimension group, namely the primitive unimodular…
We study amenable minimal Cantor systems of free groups arising from the diagonal actions of the boundary actions and certain Cantor systems. It is shown that every virtually free group admits continuously many amenable minimal Cantor…
Danz computes the depth of certain twisted group algebra extensions in Comm. Alg. (2011), which are less than the values of the depths of the corresponding untwisted group algebra extensions in Burciu et al, I.E.J.A. (2011). In this paper,…
We show that the topological complexity of an aspherical space $X$ is bounded below by the cohomological dimension of the direct product $A\times B$, whenever $A$ and $B$ are subgroups of $\pi_1(X)$ whose conjugates intersect trivially. For…
Two classes $\mathcal A$ and $\mathcal B$ of modules over a ring $R$ are said to form a cotorsion pair $(\mathcal A, \mathcal B)$ if $\mathcal A={\rm Ker Ext}^1_R(-,\mathcal B)$ and $\mathcal B={\rm Ker Ext}^1_R(\mathcal A,-)$. We…
In the paper we discuss the algebraic structure of topological full group $[[T]]$ of a Cantor minimal system $(X,T)$. We show that the topological full group $[[T]]$ has the structure similar to a union of permutational wreath products of…
Classically, an abelian group $G$ is said to be slender if every homomorphism from the countable product $\mathbb Z^{\mathbb N}$ to $G$ factors through the projection to some finite product $\mathbb Z^n$. Various authors have proposed…
We compare three definitions of the equivariant cohomological dimension of a group with operators, coming from Takasu, Adamson and Bredon relative group cohomologies, giving examples of strict inequality in all cases where it can occur. We…