Abstract
The L2-Betti numbers are related to classical Betti numbers through approximation by the normalised Betti numbers of finite index subgroups/finite coverings. We explain the (spectral) proof of this approximation theorem and briefly discuss the relation with other (homological) gradient invariants. This residually finite view will be complemented by the dynamical view in Chap. 5 and the approximation theorems for lattices in Chap. 6.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Löh, C. (2020). The Residually Nite View: Approximation. In: Ergodic Theoretic Methods in Group Homology. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-44220-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-44220-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44219-4
Online ISBN: 978-3-030-44220-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)