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18.40 (2014)

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The commutator length $\text{cl}(g)$ of $g \in [G, G]$ is the least number of commutators in $G$ whose product is $g$, and the stable commutator length is $\text{scl}(g) := \lim_{n \to \infty} \text{cl}(g^n)/n$.

Conjecture: Let $G$ be a hyperbolic group. Then the stable commutator length takes on rational values on $[G, G]$.

Contributor: D. Calegari

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