The virtual first Betti number conjecture for hyperbolic lattices

From papers

Let ΓMob(Sn)\Gamma\subset \operatorname{Mob}(\mathbb S^n) be a lattice. Virtual first Betti number conjecture. There exists a finite-index subgroup ΓΓ\Gamma'\subset\Gamma such that

H1(Γ,R)0.H^1(\Gamma',\mathbb R)\ne 0.

Equivalently, Γ\Gamma' has infinite abelianization. The source cites substantial progress for arithmetic lattices, but leaves the general conjecture open.

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Sources & referencesView supporting material

Primary source

Michael Kapovich, “Kleinian groups in higher dimensions”, arXiv:math/0701370 (2007).

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