Some questions about the dimension of a group action

C Bleak*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This article discusses three families of groups: Z≀(Z^n), PL(I^n), and PL(S^n) (the last two being the families of groups of piecewise-linear homeomorphisms of standard n-dimensional spaces). It is shown that for positive n ∈ N, Z≀(Z^n) embeds in PL(I^n), which embeds in PL(S^n). It is known that Z≀(Z^2) fails to embed in PL(I^1), and this article extends that previous result to show that Z≀(Z^2) also fails to embed in PL(S^1). The nature of the proofs of these embedding and non-embedding results hints that there may be corresponding non-embedding results in higher dimensions.
Original languageEnglish
Pages (from-to)770-776
Number of pages7
JournalBulletin of the London Mathematical Society
Issue number5
Early online date16 Jul 2008
Publication statusPublished - 1 Oct 2008


  • Embedding problems
  • Groups of homeomorphisms
  • PL Manifolds
  • R. Thompson's groups


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