Quasi-isometric rigidity for a product of lattices

Josiah Oh

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arXiv · 2512.09782

Quasi-isometric rigidity for a product of lattices

Josiah Oh

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Abstract

We demonstrate quasi-isometric rigidity for the product of a non-uniform rank one lattice and a nilpotent lattice. Specifically, we show that any finitely-generated group quasi-isometric to such a product is, up to finite noise, an extension of a non-uniform rank one lattice by a nilpotent lattice. Furthermore, we show under extra conditions that this extension is nilcentral, a notion which generalizes central extensions to extensions by a nilpotent group.

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Josiah Oh. 2025-12-10. Quasi-isometric rigidity for a product of lattices. https://arxiv.org/abs/2512.09782

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