Lück's integral torsion conjecture for residually finite 2-acyclic groups

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Let GG) be an infinite residually finite 22-acyclic group of type VFVF. Write ρ(2)(G)\rho^{(2)}(G) for its 22-torsion and ρZ(G)\rho^\mathbb{Z}(G) for its integral torsion. Lück's conjecture. One has

ρ(2)(G)=ρZ(G).\rho^{(2)}(G)=\rho^\mathbb{Z}(G).

This conjecture predicts equality between the analytic 22-torsion and the integral torsion defined through normalized torsion homology growth along Farber sequences. The paper verifies it for free-by-cyclic groups with polynomially growing monodromy, but the general statement remains open.

References

Primary source

Naomi Andrew, Sam Hughes and Monika Kudlinska, “Torsion homology growth of polynomially growing free-by-cyclic groups”, arXiv:2211.04389 (2023).

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