Geodesic
A description of $\operatorname{Aut}(dV_n)$ and $\operatorname{Out}(dV_n)$ using transducers
Luke Elliott1
1University of St Andrews, UK
Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 293-312

Voir la notice de l'article provenant de la source EMS Press

DOI

The groups dVn​ are an infinite family of groups, first introduced by C. Martínez-Pérez, F. Matucci and B. E. A. Nucinkis, which includes both the Higman–Thompson groups Vn​ (=1Vn​) and the Brin–Thompson groups nV (=nV2​). A description of the groups Aut(Gn,r​) (including the groups Gn,1​=Vn​) has previously been given by C. Bleak, P. Cameron, Y. Maissel, A. Navas, and F. Olukoya. Their description uses the transducer representations of homeomorphisms of Cantor space introduced in a paper of R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanskii, together with a theorem of M. Rubin. We generalise the transducers of the latter paper and make use of these transducers to give a description of Aut(dVn​) which extends the description of Aut(1Vn​) given in the former paper. We make use of this description to show that Out(dV2​)≅Out(V2​)≀Sd​, and more generally give a natural embedding of Out(dVn​) into Out(Gn,n−1​)≀Sd​.
DOI : 10.4171/ggd/697
Classification : 20-XX, 37-XX
Mots-clés : Brin–Thompson groups, automorphism groups, transducers, homeomorphism groups, Rubin’s theorem

Luke Elliott  1

1 University of St Andrews, UK 
Luke Elliott. A description of $\operatorname{Aut}(dV_n)$ and $\operatorname{Out}(dV_n)$ using transducers. Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 293-312. doi: 10.4171/ggd/697
@article{10_4171_ggd_697,
     author = {Luke Elliott},
     title = {A description of $\operatorname{Aut}(dV_n)$ and $\operatorname{Out}(dV_n)$ using transducers},
     journal = {Groups, geometry, and dynamics},
     pages = {293--312},
     year = {2023},
     volume = {17},
     number = {1},
     doi = {10.4171/ggd/697},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/697/}
}
TY  - JOUR
AU  - Luke Elliott
TI  - A description of $\operatorname{Aut}(dV_n)$ and $\operatorname{Out}(dV_n)$ using transducers
JO  - Groups, geometry, and dynamics
PY  - 2023
SP  - 293
EP  - 312
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/697/
DO  - 10.4171/ggd/697
ID  - 10_4171_ggd_697
ER  - 
%0 Journal Article
%A Luke Elliott
%T A description of $\operatorname{Aut}(dV_n)$ and $\operatorname{Out}(dV_n)$ using transducers
%J Groups, geometry, and dynamics
%D 2023
%P 293-312
%V 17
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/697/
%R 10.4171/ggd/697
%F 10_4171_ggd_697

Cité par Sources :