Survey on approximating L^2-invariants by their classical counterparts: Betti numbers, torsion invariants and homological growth

Abstract

In this paper we discuss open problems concerning L^2-invariants focusing on approximation by towers of finite coverings.

63 pages, Final version. To appear in EMS SURVEYS IN MATHEMATICAL SCIENCES

References in corpus (7)

• Twisting $L^2$-invariants with finite-dimensional representations
• Mahler measures and Fuglede--Kadison determinants
• Degree of $L^2$-Alexander torsion for 3-manifolds
• Three flavors of twisted invariants of knots
• Integral foliated simplicial volume of hyperbolic 3-manifolds
• Amenable covers, volume and L2-Betti numbers of aspherical manifolds
• Rank gradient in co-final towers of certain Kleinian groups

Cited by in corpus (4)

• Twisting $L^2$-invariants with finite-dimensional representations
• Mod $p$ and torsion homology growth in nonpositive curvature
• Random Walks on Graphs and Approximation of L2-Invariants
• Asymptotics of automorphic spectra and the trace formula