Lubotzky–Sarnak conjecture on property tau for hyperbolic 3-manifold groups

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Let MM be a hyperbolic 33-manifold, and let π1(M)\pi_1(M) be its fundamental group. Lubotzky–Sarnak conjecture. The group π1(M)\pi_1(M) does not have property (τ)(\tau). This is presented as a weaker conjecture related to the virtually positive Betti number conjecture. The source does not state a resolution.

References

Primary source

Mikhail Ershov, “Golod-Shafarevich groups: a survey”, arXiv:1206.0490 (2012).

Additional references

3 papers in this index state this conjecture (2008–2012). The statement above is taken from the most recent of them; the others are arXiv:1105.2389, arXiv:0804.1305.

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