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Sam Nead
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Gromov, in his monograph (see page 83 of "Essays in group theory"), writes the following.

The idea of hyperbolicity has been lingering in combinatorial group theory since the basic work by Dehn. An extensive study of a class of word hyperbolic groups $\Gamma$ with $\mathrm{dim}\, \partial \Gamma = 1$ (in the combinatorial disguise) was conducted by Olshanski (see [Ol]). Deep algebraic results on general hyperbolic groups are contained in the as yet unpublished work by I. Rips who calls them groups with negative curvature.

As you note, Gromov's earlier papers contain relevant work. Gromov also refers to Cannon's work, but only as regards rationality of certain languages. I believe that Cannon's treatment of quasi-geodesic stability, and its relevance for hyperbolic groups, slightly predates Gromov's.

Both Cannon and Gromov are alive and bothreplyboth reply to email. So perhaps it would be better to contact them directly.

Gromov, in his monograph (see page 83 of "Essays in group theory"), writes the following.

The idea of hyperbolicity has been lingering in combinatorial group theory since the basic work by Dehn. An extensive study of a class of word hyperbolic groups $\Gamma$ with $\mathrm{dim}\, \partial \Gamma = 1$ (in the combinatorial disguise) was conducted by Olshanski (see [Ol]). Deep algebraic results on general hyperbolic groups are contained in the as yet unpublished work by I. Rips who calls them groups with negative curvature.

As you note, Gromov's earlier papers contain relevant work. Gromov also refers to Cannon's work, but only as regards rationality of certain languages. I believe that Cannon's treatment of quasi-geodesic stability, and its relevance for hyperbolic groups, slightly predates Gromov's.

Both Cannon and Gromov are alive and bothreply to email. So perhaps it would be better to contact them directly.

Gromov, in his monograph (see page 83 of "Essays in group theory"), writes the following.

The idea of hyperbolicity has been lingering in combinatorial group theory since the basic work by Dehn. An extensive study of a class of word hyperbolic groups $\Gamma$ with $\mathrm{dim}\, \partial \Gamma = 1$ (in the combinatorial disguise) was conducted by Olshanski (see [Ol]). Deep algebraic results on general hyperbolic groups are contained in the as yet unpublished work by I. Rips who calls them groups with negative curvature.

As you note, Gromov's earlier papers contain relevant work. Gromov also refers to Cannon's work, but only as regards rationality of certain languages. I believe that Cannon's treatment of quasi-geodesic stability, and its relevance for hyperbolic groups, slightly predates Gromov's.

Both Cannon and Gromov are alive and both reply to email. So perhaps it would be better to contact them directly.

adde quote from gromov.
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Sam Nead
  • 28.1k
  • 5
  • 72
  • 131

Gromov, in his monograph (see page 83 of "Essays in group theory"), writes the following.

The idea of hyperbolicity has been lingering in combinatorial group theory since the basic work by Dehn. An extensive study of a class of word hyperbolic groups $\Gamma$ with $\mathrm{dim}\, \partial \Gamma = 1$ (in the combinatorial disguise) was conducted by Olshanski (see [Ol]). Deep algebraic results on general hyperbolic groups are contained in the as yet unpublished work by I. Rips who calls them groups with negative curvature.

As you note, Gromov's earlier papers contain relevant work. Gromov also refers to Cannon’s paper “The combinatorial structureCannon's work, but only as regards rationality of cocompact discrete hyperbolic groups”certain languages. He also credits small cancellation theory I believe that Cannon's treatment of quasi-geodesic stability, and Dehn’s workits relevance for hyperbolic groups, slightly predates Gromov's.

Both Cannon and Gromov are alive and bothreply to email. So perhaps it would be better to contact them directly.

Gromov refers to Cannon’s paper “The combinatorial structure of cocompact discrete hyperbolic groups”. He also credits small cancellation theory, and Dehn’s work.

Gromov, in his monograph (see page 83 of "Essays in group theory"), writes the following.

The idea of hyperbolicity has been lingering in combinatorial group theory since the basic work by Dehn. An extensive study of a class of word hyperbolic groups $\Gamma$ with $\mathrm{dim}\, \partial \Gamma = 1$ (in the combinatorial disguise) was conducted by Olshanski (see [Ol]). Deep algebraic results on general hyperbolic groups are contained in the as yet unpublished work by I. Rips who calls them groups with negative curvature.

As you note, Gromov's earlier papers contain relevant work. Gromov also refers to Cannon's work, but only as regards rationality of certain languages. I believe that Cannon's treatment of quasi-geodesic stability, and its relevance for hyperbolic groups, slightly predates Gromov's.

Both Cannon and Gromov are alive and bothreply to email. So perhaps it would be better to contact them directly.

Source Link
Sam Nead
  • 28.1k
  • 5
  • 72
  • 131

Gromov refers to Cannon’s paper “The combinatorial structure of cocompact discrete hyperbolic groups”. He also credits small cancellation theory, and Dehn’s work.