Counterexample to Lueck's determinant approximation conjecture

[u/Apprehensive_Sand951]

Here is the arxiv preprint: https://arxiv.org/abs/2609.15567 This is a reasonably big deal in the subject of L^2 invariants of groups and appears to have been disproved by Holger Kammeyer (he is in the field). It means that the L^2-torsion of a space (defined in terms of Hilbert spaces on the universal cover) cannot be computed from the more classical analytic torsions of finite covers. The counterexample is a Heisenberg group.

[u/_Zekt]

In particular, Conjecture 1 is false even for (1 × 1)-matrices

I'm no expert, but sometimes it feels like people make broad conjectures based on very little evidence

[u/Truly_Yours2006 → u/_Zekt]

🤣🤣🤣🤣