Continuously many quasiisometry classes of 2-generator groups

@article{Bowditch1998ContinuouslyMQ,
  title={Continuously many quasiisometry classes of 2-generator groups},
  author={Brian H. Bowditch},
  journal={Commentarii Mathematici Helvetici},
  year={1998},
  volume={73},
  pages={232-236}
}
  • B. Bowditch
  • Published 30 June 1998
  • Mathematics
  • Commentarii Mathematici Helvetici
Abstract. We construct continuously many quasiisometry classes of torsion-free 2-generator small cancellation groups.  
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References

SHOWING 1-3 OF 3 REFERENCES
Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means
This paper gives a negative solution to the problem of Milnor concerning the degrees of growth of groups. The construction also answers a question of Day concerning amenable groups. A number of other
Combinatorial Group Theory
Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.
Gromov , Asymptotic invariants of infinite groups
  • Izv . Acad . Nauk SSSR , Ser . Mat .
  • 1984