Abstract:We prove a variety of results about subgroups of Thompson's group $V$. First we prove that every action graph of a finitely generated subgroup of $V$ acting on an orbit in Cantor space is quasi-isometric to a tree. Then we prove that for a broad class of groups of homeomorphisms of the real line, for example Thompson's group $F$, any action on the Cantor space via an embedding into Thompson's group $V$ must be semiconjugate to the standard action on the line. Finally, we use this to establish that many such groups cannot embed into $V$; in particular the Stein group $F_{2,3}$ cannot embed in $V$, answering a question of the third author.
From: Matthew Zaremsky [view email]
[v1]
Tue, 19 May 2026 23:48:07 UTC (24 KB)
[v2]
Fri, 29 May 2026 01:47:04 UTC (24 KB)
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