Whitehead conjecture

The Whitehead conjecture is a claim in algebraic topology. It was formulated by J. H. C. Whitehead in 1941. It states that every connected subcomplex of a two-dimensional aspherical CW complex is aspherical.

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.

References

J. H. C. Whitehead, On adding relations to homotopy groups, Annals of Mathematics, 2nd Ser., 42 (1941), no. 2, 409 –428.
Mladen Bestvina, Noel Brady, Morse theory and finiteness properties of groups, Inventiones Mathematicae 129 (1997), no. 3, 445 – 470.

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