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A characterization of cocompact hyperbolic and finite-volume hyperbolic groups in dimension three


Authors: J. W. Cannon and Daryl Cooper
Journal: Trans. Amer. Math. Soc. 330 (1992), 419-431
MSC: Primary 22E40; Secondary 30F40, 53C70, 57M15
MathSciNet review: 1036000
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Abstract: We show that a cocompact hyperbolic group in dimension $ 3$ is characterized by certain properties of its word metric which depend only on the group structure and not on any action on hyperbolic space. We prove a similar theorem for finite-volume hyperbolic groups in dimension $ 3$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1036000-0
Article copyright: © Copyright 1992 American Mathematical Society