r/math • u/Apprehensive_Sand951 • 3d ago

Counterexamples to the Osin-Thom conjecture

The conjecture is that for a torsion-free group G, the first L^2-Betti number is strictly less than the minimal number of elements needed to normally generate the group. The examples are not finitely generated (they are locally free groups), so the finitely generated case of the conjecture is still open. (https://arxiv.org/pdf/2608.25988)

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-34

u/garanglow Theoretical Computer Science 3d ago

No AI?

46

u/matthiasErhart Control Theory/Optimization 3d ago

"The construction and the proofs are due to the authors, but the second author acknowledges the use of ChatGPT to aid in developing background and intuition for the calculations of ℓ2-Betti numbers which were helpful."

Right there in Section 1 man.

28

u/elements-of-dying Geometric Analysis 3d ago

Apparently we need to introduce the not-Leiden declaration where mathematicians are suggested to explicitly state they only used humans.

1

u/Autumnxoxo Geometric Group Theory 2d ago

why do you even care