Related papers: The Even Isomorphism Theorem for Coxeter Groups

We state and prove a Cheeger-like inequality for coexact 1-forms on closed orientable Riemannian manifolds.

We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

This paper offers a proof of the Coase theorem by formalizing the notion of ideal exchanges.

We prove Schlichting's theorem for approximate subgroups: if $\mathcal{X}$ is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an invariant approximate subgroup commensurable with…

We introduce stable reflection length in Coxeter groups, as a way to study the asymptotic behaviour of reflection length. This creates connections to other well-studied stable length functions in groups, namely stable commutator length and…

This is a survey of some aspects of the large-scale geometry of right-angled Coxeter groups. The emphasis is on recent results on their negative curvature properties, boundaries, and their quasi-isometry and commensurability classification.

We prove the ergodic Closing Lemma for Nonsingular Endomorphisms.

We prove that polycyclic groups are of polynomial growth or of uniform exponential growth.

Let $C(T)$ be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either $B_n$ or $D_n$. Let $C_Y(T)$ be a natural quotient of $C(T)$, and if $C(T)$ is simply-laced (which means all the relations…

We derive presentations of the interval groups related to all quasi-Coxeter elements in the Coxeter group of type $D_n$. Type $D_n$ is the only infinite family of finite Coxeter groups that admits proper quasi-Coxeter elements. The…

We prove Union-Closed sets conjecture.

We review the properties of the finite Coxeter groups which are most useful for applications to cohomological invariants, namely their classes of involutions and their "cubes" (abelian subgroups generated by reflections).

The evenness conjecture for the equivariant unitary bordism groups states that these bordism groups are free modules over the unitary bordism ring on even-dimensional generators. In this paper we review the cases in which the conjecture is…

We generalize the Cauchy-Davenport theorem to locally compact groups.

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we…

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…

In this note we verify the equivalent version of Huppert's conjecture for $K_3$-groups.

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…