Wang tiles are square tiles with colored edges. We construct an aperiodic set of Wang tiles that is strongly deterministic in the sense that any two adjacent edges of a tile determine the tileâ€¦ (More)

Let G, F be finitely generated groups with infinitely many ends and let Ï€1(Î“,A), Ï€1(âˆ†,B) be graph of groups decompositions of F, G such that all edge groups are finite and all vertex groups have atâ€¦ (More)

It is shown that D. Cohenâ€™s inequality bounding the isoperimetric function of a group by the double exponential of its isodiametric function is valid in the more general context of locally finiteâ€¦ (More)

We show that locally connected, simply connected homogeneous continua are not separated by arcs. We ask several questions about homogeneous continua which are inspired by analogous questions inâ€¦ (More)

In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and sâ€² with sâ€² < s, are Î´-hyperbolic with Î´ = O(s). We also show that theâ€¦ (More)

We show that the if the isoperimetric profile of a bounded genus non-compact surfaces grows faster than âˆš t, then it grows at least as fast as a linear function. This generalizes a result of Gromovâ€¦ (More)

It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show thatâ€¦ (More)