On the top-dimensional $\ell^2$-Betti numbers
Abstract
The purpose of this note is to introduce a trick which relates the (non)-vanishing of the top-dimensional -Betti numbers of actions with that of sub-actions. We provide three different types of applications: we prove that the -Betti numbers of Aut() and Out() (and of their Torelli subgroups) do not vanish in degree equal to their virtual cohomological dimension, we prove that the subgroups of the 3-manifold groups have vanishing -Betti numbers in degree 3 and 2 and we prove for instance that has ergodic dimension .
Cite
@article{arxiv.1909.01633,
title = {On the top-dimensional $\ell^2$-Betti numbers},
author = {Damien Gaboriau and Camille Noûs},
journal= {arXiv preprint arXiv:1909.01633},
year = {2022}
}
Comments
''Camille No\^us'' is a scientific consortium created to affirm the collaborative and open nature of knowledge creation and dissemination, under the control of the academic community. This scientific collective, like Bourbaki, H. P. de Saint Gervais or A. Besse in mathematics takes on the identity of a scientific personality who embodies the collective contribution of the academic community