Dynamical correspondences of $L^2$-Betti numbers

Bingbing Liang

doi:10.4171/ggd/480

JournalsggdVol. 13, No. 1pp. 89–106

Dynamical correspondences of $L^{2}$ -Betti numbers

Bingbing Liang
Max-Planck-Institut für Mathematik, Bonn, Germany

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Abstract

We investigate dynamical analogues of the $L^{2}$ -Betti numbers for modules over integral group ring of a discrete sofic group. In particular, we show that the $L^{2}$ -Betti numbers exactly measure the failure of addition formula for dynamical invariants.

Cite this article

Bingbing Liang, Dynamical correspondences of $L^{2}$ -Betti numbers. Groups Geom. Dyn. 13 (2019), no. 1, pp. 89–106

DOI 10.4171/GGD/480