Free Lamplighter Groups and a Question of Atiyah

Abstract

We compute the von Neumann dimensions of the kernels of adjacency operators on free lamplighter groups and show that they are irrational, thus providing an elementary constructive answer to a question of Atiyah.

AMSLaTeX, 10 pages, to appear in Amer J Math

References in corpus (5)

• Rational group ring elements with kernels having irrational dimension
• On Turing dynamical systems and the Atiyah problem
• Closed manifolds with transcendental L2-Betti numbers
• On the spectrum of lamplighter groups and percolation clusters
• On the Eigenspaces of Lamplighter Random Walks and Percolation Clusters on Graphs

Cited by in corpus (9)

• Rational group ring elements with kernels having irrational dimension
• On Turing dynamical systems and the Atiyah problem
• Closed manifolds with transcendental L2-Betti numbers
• Group ring elements with large spectral density
• Mean Dimension, Mean Rank, and von Neumann-Lück Rank
• Vanishing of l^2-cohomology as a computational problem
• On computing homology gradients over finite fields
• On the lattice of subgroups of the lamplighter group
• The realization problem for some wild monoids and the Atiyah problem