Answers are grounded in this paper and cite their sources.
Given a short exact sequence of finitely generated groups \[ 1 → K → G → H → 1 \] it is known that if K and G are word hyperbolic, and if K is nonelementary, then H is word hyperbolic. In the original examples due to Thurston, as well as later examples due to Bestvina and Feighn, the group H is elementary. We give a method for constructing examples where all three groups are nonelementary.
No takes yet. Share an insight, caveat, or question.
Lee Mosher (1997) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: