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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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 $3$.
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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