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

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- by J. W. Cannon and Daryl Cooper
- Trans. Amer. Math. Soc.
**330**(1992), 419-431 - DOI: https://doi.org/10.1090/S0002-9947-1992-1036000-0
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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 $3$.## References

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## Bibliographic Information

- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**330**(1992), 419-431 - MSC: Primary 22E40; Secondary 30F40, 53C70, 57M15
- DOI: https://doi.org/10.1090/S0002-9947-1992-1036000-0
- MathSciNet review: 1036000