Geodesic
Tarski numbers of group actions
Gili Golan1 orcid
1Bar-Ilan University, Ramat Gan, Israel
Groups, geometry, and dynamics, Tome 10 (2016) no. 3, pp. 933-950

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DOI

The Tarski number of a group action G↷X is the minimal number of pieces in a paradoxical decomposition of it. In this paper we solve the problem of describing the set of Tarski numbers of group actions. Namely, for any k≥4 we construct a faithful transitive action of a free group with Tarski number k. We also construct a group action G↷X with Tarski number 6 such that the Tarski numbers of restrictions of this action to finite index subgroups of G are arbitrarily large.
DOI : 10.4171/ggd/371
Classification : 43-XX, 05-XX, 20-XX
Mots-clés : Tarski number, paradoxical decomposition, amenability, Stallings core

Gili Golan  1

1 Bar-Ilan University, Ramat Gan, Israel 
Gili Golan. Tarski numbers of group actions. Groups, geometry, and dynamics, Tome 10 (2016) no. 3, pp. 933-950. doi: 10.4171/ggd/371
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     title = {Tarski numbers of group actions},
     journal = {Groups, geometry, and dynamics},
     pages = {933--950},
     year = {2016},
     volume = {10},
     number = {3},
     doi = {10.4171/ggd/371},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/371/}
}
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