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

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

scl(anb1apbaqb1arb)=1gcd(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.

Sources & referencesView supporting material

Primary source

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

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