A finitely generated counterexample to Eilenberg–Ganea at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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A finitely generated counterexample to Eilenberg–Ganea

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	symmetry	Levels:	1
Category:	Group theory	Lean version:	YES! ✔
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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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LEVEL 1 A finitely generated counterexample to the Eilenberg–Ganea conjecture

released 2026-09-23 | 2 theorems · 11 lemmas · 14 proofs · 12,185 words | PLAY LEVEL 1 » (pdf)

We construct a finitely generated residually finite group of integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture.

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