The Eilenberg–Ganea conjecture is a claim in algebraic topology.
It was formulated by Samuel Eilenberg and Tudor Ganea in 1957, in a short, but influential paper.
It states that if a group G has cohomological dimension 2, then it has a 2-dimensional Eilenberg–MacLane space
For n different from 2, a group G of cohomological dimension n has an n-dimensional Eilenberg–MacLane space.
It is also known that a group of cohomological dimension 2 has a 3-dimensional Eilenberg−MacLane space.