25 citations · 106 across the 38 of their papers we have counts for
5 papers · 1 filter
Metrics on diagram groups and uniform embeddings in a Hilbert space
Goulnara Arzhantseva, Victor Guba, Mark Sapir
We give first examples of finitely generated groups having an intermediate, with values in (0,1), Hilbert space compression (which is a numerical parameter measuring the distortion…
Groups with small Dehn functions and bipartite chord diagrams
Alexander Olshanskii, Mark Sapir
We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function and other small Dehn functions. Some of…
Relatively Hyperbolic Groups with Rapid Decay Property
Cornelia Drutu, Mark Sapir
We prove that a finitely generated group hyperbolic relative to the collection of finitely generated subgroups H_1,..., H_m has the Rapid Decay property if and only if each H_i…
Non-linear residually finite groups
Cornelia Drutu, Mark Sapir
We give the first example of a non-linear residually finite 1-related group: < a, t | a^{t^2}=a^2>.
Tree-graded spaces and asymptotic cones of groups
Cornelia Drutu, Mark Sapir
We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization…