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Conjugator length in Thompson's groups (2101.10316v3)
Published 25 Jan 2021 in math.GR
Abstract: We prove Thompson's group $F$ has quadratic conjugator length function. That is, for any two conjugate elements of $F$ of length $n$ or less, there exists an element of $F$ of length $O(n2)$ that conjugates one to the other. Moreover, there exist conjugate pairs of elements of $F$ of length at most $n$ such that the shortest conjugator between them has length $\Omega(n2)$. This latter statement holds for $T$ and $V$ as well.