The action of the Thompson group F on infinite trees

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We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the action of F by translations on one of its homogeneous spaces, F/H_2, corresponding to a certain subgroup H_2 of F. The representation of F on the Hilbert space l^2(F/H_2) is faithful on the complex group algebra C[F].
Original languageEnglish
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Issue number3
Pages (from-to)359-370
Publication statusPublished - Dec 2022


  • Thompson's group F
  • infinite trees
  • equivariant compactification
  • Thompson’s group F


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