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Eilenberg–Ganea conjecture
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 ''K''(''G'', 1). 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.
In 1997, Mladen Bestvina and Noel Brady constructed a group ''G'' so that either ''G'' is a counterexample to the Eilenberg–Ganea conjecture, or there must be a counterexample to the Whitehead conjecture.
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