Whitehead conjecture

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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.


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