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Quasi-isometric recognition of virtually polycyclic groups
Proves that every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic, resolving the Eskin–Fisher–Whyte lattice-recognition conjecture. Equivalently, a group quasi-isometric to a lattice in a connected simply connected solvable Lie group is virtually a uniform lattice in some such Lie group, possibly a different one.
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Quasi-isometric recognition of virtually polycyclic groups
Sep 24, 2026·paper.pdf
We prove that every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic. This resolves the lattice-recognition conjecture of Eskin, Fisher and Whyte, which allows the ambient solvable Lie group in the conclusion to differ from the one in the hypothesis.