Cubulating small cancellation free products

Free Subgroups of Small Cancellation Groups

with the property that for any pair r, s of elements of R either r = s or there is very little free cancellation in forming the product rs. The classical example of such a group is the fundamental group of a closed orientable 2-manifold of genus k. The study of this group has given rise both to the theory of one-relator groups, initiated by Magnus ([3]), and to the theory of small cancellation ...

Cubulating Graphs of Free Groups with Cyclic Edge Groups

We prove that if G is a group that splits as a finite graph of finitely generated free groups with cyclic edge groups, and G has no non-Euclidean Baumslag-Solitar subgroups, then G is the fundamental group of a compact nonpositively curved cube complex. In addition, if G is also wordhyperbolic (i.e., if G contains no Baumslag-Solitar subgroups of any type), we show that G is linear (in fact, is...

Cubulating spaces with walls

The elegant notion of a space with walls was introduced by Haglund and Paulin [6]. Prototypical examples of spaces with walls are CAT(0) cube complexes, introduced by Gromov in [5]. The purpose of this note is to observe that every space with walls has a canonical embedding in a CAT(0) cube complex and, consequently, a group action on a space with walls extends naturally to a group action on a ...

Geometric small cancellation

A General Small Cancellation Theory

In this article a generalized version of small cancellation theory is developed which is applicable to specific types of high-dimensional simplicial complexes. The usual results on small cancellation groups are then shown to hold in this new setting with only slight modifications. For example, arbitrary dimensional versions of the Poincaré construction and the Cayley complex are described.