We study actions of countable discrete groups which are Monotileable amenable groups in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first l2-Betti number of G with that of the stabilizer subgroups.
Cite this paper
Gaweash, A. M. A. , Bakur, H. Y. I. and Mulla, M. A. M. (2021). Monotileable Amenable Groups: An Application. Open Access Library Journal, 8, e7012. doi: http://dx.doi.org/10.4236/oalib.1107012.
Brown, N.P. and Ozawa, N. (2008) C*-Algebras and Finite-Dimensional Approximations. Graduate Studies in Mathematics, 88.
https://doi.org/10.1090/gsm/088