Automatic structures, rational growth, and geometrically finite hyperbolic groups
From MaRDI portal
Publication:1895679
DOI10.1007/BF01241129zbMath0831.20041arXivmath/9401201MaRDI QIDQ1895679
Walter D. Neumann, Michael Shapiro
Publication date: 6 February 1996
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9401201
geodesicsregular languagescuspsgeometrically finite hyperbolic groupsmaximal parabolic subgroupsbiautomatic structuresreal hyperbolic spacesrational growth functionssynchronous automatic structures
Formal languages and automata (68Q45) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)
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Cites Work
- Unnamed Item
- Unnamed Item
- The combinatorial structure of cocompact discrete hyperbolic groups
- Rational subgroups of biautomatic groups
- Automatic groups and amalgams
- Geometrical finiteness for hyperbolic groups
- A note on curvature and fundamental group
- The Hadamard-Cartan theorem in locally convex metric spaces
- DETERMINISTIC AND NON-DETERMINISTIC ASYNCHRONOUS AUTOMATIC STRUCTURES
- EQUIVALENT AUTOMATIC STRUCTURES AND THEIR BOUNDARIES
- AUTOMATIC STRUCTURES AND BOUNDARIES FOR GRAPHS OF GROUPS