Related papers: The Virtually Cyclic Classifying Space of the Heis…

We prove that if a countable discrete group $\Gamma$ is {\it w-rigid}, i.e. it contains an infinite normal subgroup $H$ with the relative property (T) (e.g. $\Gamma= SL(2,\Bbb Z) \ltimes \Bbb Z^2$, or $\Gamma = H \times H'$ with $H$ an…

We investigate strictly developable simple complexes of groups with arbitrary local groups, or equivalently, group actions admitting a strict fundamental domain. We introduce a new method for computing the cohomology of such groups. We also…

By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…

We study the harmonic space of line bundle valued forms over a covering manifold with a discrete group action $\Gamma$, and obtain an asymptotic estimate for the $\Gamma$-dimension of the harmonic space with respect to the tensor times $k$…

We study graded connected algebras over a field of characteristic zero and give an explicit formula for the cyclic homology of a tensor algebra. By means of a slightly new definition of David Anick's notion "strongly free" we are able to…

The representation dimension was defined by M. Auslander in 1970 and is, due to spectacular recent progress, one of the most interesting homological invariants in representation theory. The precise value is not known in general, and is very…

We investigate the structure of the minimal displacement set in $8$-located complexes with the SD'-property. We show that such set embeds isometrically into the complex. Since $8$-location and simple connectivity imply Gromov hyperbolicity,…

We study the $S_3$-orbifold of a rank three Heisenberg vertex algebras in terms of generators and relations. By using invariant theory we prove that the orbifold algebra has a minimal strongly generating set of vectors whose conformal…

We use the cluster variation method (CVM) and Monte Carlo simulations to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. This model corresponds to the usual three-dimensional cubic Ising…

Let X be an arbitrary hyperbolic geodesic metric space and let G be a countable non-elementary weakly acylindrical group of isometries of X. We show that the second bounded cohomology group of G with real coefficients or with coefficients…

For a totally real field F of degree d>1 and a quadratic space V of signature (m,2)^{d_+} x (m+2,0)^{d-d_+} with associated Shimura variety Sh(V), we consider the subring of cohomology generated by the classes of weighted special cycles. We…

A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…

Dieter Happel asked the following question: If the $n$-th Hochschild cohomology group of a finite dimensional algebra $\Gamma$ over a field vanishes for all sufficiently large $n$, is the global dimension of $\Gamma$ finite? We give a…

Let $\Gamma$ be a discrete group. Assuming rational injectivity of the Baum-Connes assembly map, we provide new lower bounds on the rank of the positive scalar curvature bordism group and the relative group in Stolz' positive scalar…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

We have compared numerical simulations to observations for the nearby (< 40 Mpc) groups of galaxies (Huchra & Geller 1982 and Ramella et al. 2002). The group identification is carried out using a group-finding algorithm developed by Huchra…

We compute the $G$-equivariant homotopy type of the real topological cyclic homology of spherical group rings with anti-involution induced by taking inverses in the group, where $G$ denotes the group $Gal(\mathbb{C}/\mathbb{R})$. The real…

We prove that any region $\Gamma$ in a homogeneous $n$-dimensional and locally compact separable metric space $X$, where $n\geq 2$, cannot be irreducibly separated by a closed $(n-1)$-dimensional subset $C$ with the following property: $C$…

We give a classification of integral lattices with virtually abelian symmetry group. As a consequence, we complete the classification of K3 surfaces with virtually abelian automorphism group. In the appendix we formulate an algorithm for…

We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields…