The EilenbergâGanea 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 EilenbergâMacLane space . For n different from 2, a group G of cohomological dimension n has an n-dimensional EilenbergâMacLane space. It is also known that a group of cohomological dimension 2 has a 3-dimensional EilenbergâMacLane space.
In 1997, Mladen Bestvina and Noel Brady constructed a group G so that either G is a counterexample to the EilenbergâGanea conjecture, or there must be a counterexample to the Whitehead conjecture; in other words, it is not possible for both conjectures to be true..