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A finitely generated Eilenberg–Ganea counterexample
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.
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A finitely generated counterexample to the Eilenberg–Ganea conjecture
Sep 23, 2026·paper.pdf
We construct a finitely generated residually finite group of integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture.