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arXiv · 1107.0672

Centralizers in R. Thompson's group V_n

Collin Bleak·Hannah Bowman·Alison Gordon·Garrett Graham·Jacob Hughes·Francesco Matucci·Jenya Sapir
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Abstract

Let n be bigger than 1 and let A be an element in the Higman-Thompson group V_n. We study the structure of the centralizer of a in V_n through a careful analysis of the action of the group generated by A on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks to assist us in our analysis. A consequence of our structure theorem is that centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in V_n.

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Collin Bleak, Hannah Bowman, Alison Gordon, Garrett Graham, Jacob Hughes, Francesco Matucci, Jenya Sapir. 2011-07-04. Centralizers in R. Thompson's group V_n. https://arxiv.org/abs/1107.0672

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