Lück–Sauer–Wegner conjecture on measure-equivalent groups and L2-torsion

From papers

Let Γ\Gamma and Λ\Lambda be det-L2L^2-acyclic groups, meaning that their L2L^2-torsion is defined. Assume that Γ\Gamma and Λ\Lambda are measure equivalent of index cc.

Lück–Sauer–Wegner conjecture. Their L2L^2-torsions satisfy

ρ(2)(Γ)=cρ(2)(Λ).\rho^{(2)}(\Gamma)=c\cdot\rho^{(2)}(\Lambda).

This conjecture proposes that L2L^2-torsion transforms by the measure-equivalence index, in analogy with the scaling formula for L2L^2-Betti numbers. The supplied text does not state whether the conjecture has been resolved.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Holger Kammeyer, “L2-invariants of nonuniform lattices in semisimple Lie groups”, arXiv:1309.1033 (2013).

Solutions 0

No solutions have been posted yet.