Cornelia Drutu

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We construct finitely generated groups with arbitrary prescribed Hilbert space compression α ∈ [0, 1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 3, hence they(More)
Divergence functions of a metric space estimate the length of a path connecting two points A, B at distance ≤ n avoiding a large enough ball around a third point C. We characterize groups with non-linear divergence functions as groups having cut-points in their asymptotic cones. That property is weaker than the property of having Morse (rank 1)(More)
We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with nonrelatively hyperbolic peripheral(More)
Preface The main goal of this book is to describe several tools of the quasi-isometric rigidity and to illustrate them by presenting (essentially self-contained) proofs of several fundamental theorems in this area: Gromov's theorem on groups of polynomial growth, Mostow Rigidity Theorem and Schwartz's quasi-isometric rigidity theorem for nonuniform lattices(More)