Related papers: Simple archimedean dimension groups

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the…

We compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the…

We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…

We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective…

Let $G$ be a split connected reductive group defined over a nonarchimedean local field of residual characteristic $p$, and let $\mathcal{H}$ be the pro-$p$-Iwahori--Hecke algebra associated to a fixed choice of pro-$p$-Iwahori subgroup. We…

In this note we investigate the simplicial volume of fiber bundles with connected structure group. We are able to show that if the structure group is either compact or a Lie group, or if the fiber is aspherical that the simplicial volume of…

Given a simplicial complex we associate to it a squarefree monomial ideal which we call the face ideal of the simplicial complex, and show that it has linear quotients. It turns out that its Alexander dual is a whisker complex. We apply…

We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group.…

We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on AF C*-algebras. Our main result…

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…

In view of solving problems of geometric realizability of polyhedra with given geometric constraints, we describe the space of geometric realizations of a simply-connected triangulated euclidean polyhedron in $\mathbb{R}^3$ up to similarity…

We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian…

We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…

In this paper we investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a…

This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated…

We give a uniform construction of the finite simple groups $E_6(q)$, $F_4(q)$ and ${}^2E_6(q)$, which does not require any special treatment for characteristics 2 or 3, and in particular avoids any mention of quadratic Jordan algebras.…

Let $G$ be a countable infinite amenable group and $P$ be a polyhedron. We give a construction of minimal subshifts of $P^G$ with arbitrarily mean topological dimension less than $\dim P$.

We describe the full group of isometries of each left invariant Riemannian metric on the simply connected unimodular nilpotent or solvable $(R)$-type Lie groups of dimension four.

We show that a monomial ideal $I$ has projective dimension $\leq$ 1 if and only if the minimal free resolution of $S/I$ is supported on a graph that is a tree. This is done by constructing specific graphs which support the resolution of the…

We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.