Virtually nilpotent groups are coarse median if and only if virtually abelian, via sub-Riemannian obstruction in the asymptotic cone, completing a lattice classification.
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Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.
citing papers explorer
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Coarse median property of virtually nilpotent groups
Virtually nilpotent groups are coarse median if and only if virtually abelian, via sub-Riemannian obstruction in the asymptotic cone, completing a lattice classification.
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Thurston norm, polytopes and splitting complexity
Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.