We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. Thisâ€¦ (More)

By studying connectedness at infinity of systolic groups we distinguish them from some other classes of groups, in particular from the fundamental groups of manifolds covered by euclidean space ofâ€¦ (More)

In this article, we introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. This class of complexes is closed under Cartesianâ€¦ (More)

The notion of k-systolic (k â‰¥ 6 being a natural number) complexes was introduced by T. Januszkiewicz and J. ÅšwiaÌ§tkowski [JS1] and, independently, by F. Haglund [H] as combinatorial analogue ofâ€¦ (More)

We characterize 2â€“dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of aâ€¦ (More)

We characterize 2â€“dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of aâ€¦ (More)

We prove the Haagerup property (= Gromovâ€™s a-T-menability) for finitely generated groups defined by infinite presentations satisfying the Câ€²(1/6)â€“small cancellation condition. We deduce that theseâ€¦ (More)

We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. Corollary: the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.â€¦ (More)