The stable commutator length formula for a family of words in F2F_2

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Let p,q,r∈Np,q,r\in\mathbb{N} and set n=p+q+rn=p+q+r. Stable commutator length formula. Then

scl⁡(a−nb−1apbaqb−1arb)=1−gcd⁡(n,q)2n.\operatorname{scl}(a^{-n} b^{-1} a^p b a^q b^{-1} a^r b)=1-\frac{\gcd(n,q)}{2n}.

The paper presents this as an unrelated conjecture at its conclusion. No resolution or partial result is supplied in the given text.

References

Primary source

Lukas Brantner, “On the Complexity of Sails”, arXiv:1102.1365 (2011).

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