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arXiv · 2205.06071

On Whitehead's cut vertex lemma

Rylee Alanza Lyman
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Abstract

One version of Whitehead's famous cut vertex lemma says that if an element of a free group is part of a free basis, then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut vertex. We state and prove a version of this lemma for conjugacy classes of elements and convex-cocompact subgroups of groups acting cocompactly on trees with finitely generated edge stabilizers.

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Rylee Alanza Lyman. 2022-05-12. On Whitehead's cut vertex lemma. https://doi.org/10.1515/jgth-2022-0089

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