Constructs a finitely generated residually finite group with integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture. It has no two-dimensional classifying space, even with infinitely many cells. (Lean)
Manuscript
A finitely generated counterexample to the Eilenberg–Ganea conjecture
September 23, 2026 · source · cite as \cite{OAI:A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026}
We construct a finitely generated residually finite group of integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture.
Result 249 · Group theory. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md