Automorphism towers of groups of homeomorphisms of Cantor space

Olukoya, Feyishayo

Abstract

We show that for any full and sufficiently transitive (i.e., flexible) group G of homeomorphisms of Cantor space, Aut(Aut(G)) = Aut(G). This class contains many generalisations of the Higman-Thompson g roups Gn,r, and the Rational group R2
of Grigorchuk, Nekrashevych, and Sushchanskiĭ. We also demonstrate that for generalisations Tn,r of R. Thompson’s group T, Aut(Aut(Tn,r)) = Aut(Tn,r). In the case of the groups Gn,r and Tn,r our results extend results of Brin and Guzmán for Thompson’s group T, and generalisations of Thompson’s group F.

Citation

Olukoya, F. (2021). Automorphism towers of groups of homeomorphisms of Cantor space. Israel Journal of Mathematics, 244(2), 883-899. https://doi.org/10.1007/s11856-021-2196-z

• Journal Article Type: Article
• Acceptance Date: Sep 9, 2021
• Publication Date: 2021-09
• Deposit Date: Jun 5, 2023
• Journal: ISRAEL JOURNAL OF MATHEMATICS
• Print ISSN: 0021-2172
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 244
• Issue: 2
• Pages: 883-899
• DOI: https://doi.org/10.1007/s11856-021-2196-z