Let Î“ be a finitely generated group. Given a finite set of generators S of Î“, the word length lS(Î³) for an element Î³ âˆˆ Î“ is defined to be the smallest positive integer for which there exist s1, Â· Â· Â·â€¦ (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, inâ€¦ (More)

Let G be a Lie group and Î“ be a discrete subgroup. We show that if {Î¼n} is a convergent sequence of probability measures on G/Î“ which are invariant and ergodic under actions of unipotentâ€¦ (More)

Following Gromov, the coboundary expansion of building-like complexes is studied. In particular, it is shown that for any n â‰¥ 1, there exists a constant (n) > 0 such that for any 0 â‰¤ k < n the k-thâ€¦ (More)

We introduce a new geometric tool for analyzing groups of finite au-tomata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff theâ€¦ (More)

Divergence functions of a metric space estimate the length of a path connecting two points A, B at distance â‰¤ n avoiding a large enough ball around a third point C. We characterize groups withâ€¦ (More)

A CAT(âˆ’1)-space is a metric geodesic space in which every geodesic triangle is thinner than its associated comparison triangle in the hyperbolic plane ([B], [BriHa], [Gr]). The CAT(âˆ’1)-property isâ€¦ (More)

Let G and H âŠ‚ G be connected reductive real algebraic groups defined over Q, and admitting no nontrivial Q-characters. Let Î“ âŠ‚ G(Q) be an arithmetic lattice in G, and Ï€ : Gâ†’ Î“\G be the naturalâ€¦ (More)