The Eilenberg-Ganea conjecture asserts that a group of integral cohomological dimension 2 has geometric dimension 2. In other words, it asks for a two-dimensional CW-complex with that fundamental group and contractible universal cover. The model need not have finitely many cells. The dimensions here are ordinary group dimensions, rather than dimensions for proper actions or for a specified family of subgroups.
Eilenberg-Ganea Conjecture
See also
Classifying Space, Cohomological Dimension, Geometric DimensionExplore with Wolfram|Alpha
References
Davis, M. W. "Poincaré Duality Groups." In Surveys on Surgery Theory, Vol. 1 (Ed. S. Cappell, A. Ranicki, and J. Rosenberg). Princeton, NJ: Princeton University Press, pp. 167-194, 2000. https://math.osu.edu/~davis.12/pdgroup.pdf.Cite this as:
Weisstein, Eric W. "Eilenberg-Ganea Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Eilenberg-GaneaConjecture.html