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of ends of a group; hyperbolicity of a group ; the homeomorphism type. Shalom, Orbit equivalence rigidity and bounded cohomology. Books and monographs edit These texts cover geometric group theory and related topics. Mikhail Gromov, "Asymptotic invariants of infinite groups", in "Geometric Group Theory Vol. The study of relatively hyperbolic groups gained prominence in the 2000s. (Russian) Izvestial Rossiyskoi Akademii Nauk Seriya Matematicheskaya, vol. Shapiro, editors, Geometric Group Theory Down Under, pages 119-137, Berlin, 1999.
Journal of the American Mathematical Society, vol. A particularly important development here is the work of Gromov who used probabilistic methods to prove 46 the existence of a finitely generated group that is not uniformly embeddable into a Hilbert space. Topology of the complement of real hyperplanes.
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Springer-Verlag, Berlin-New York, 1980. Advances in Mathematics, vol. The study of amenability and of groups whose amenability status is still unknown. Interactions with mathematical logic and the study of first-order theory of free groups. 3224; translation in Izvestiya. Translated from the 1977 French original by John Stillwell. This direction was initiated by the work of Schwartz on quasi-isometric rigidity of rank-one lattices 18 and the work of Farb the paper writing service and Mosher on quasi-isometric rigidity of Baumslag-Solitar groups. Journal of the American Mathematical Society, 8(3 597-627, 1995. Injective maps between Artin groups. Handel, Train tracks and automorphisms of free groups.