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The **Whitehead conjecture** (also known as the **Whitehead asphericity 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.

A group presentation is called *aspherical* if the two-dimensional CW complex associated with this presentation is aspherical or, equivalently, if . The Whitehead conjecture is equivalent to the conjecture that every sub-presentation of an aspherical presentation 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; in other words, it is not possible for both conjectures to be true.

- Whitehead, J. H. C. (1941). "On adding relations to homotopy groups".
*Annals of Mathematics*. 2nd Ser.**42**(2): 409–428. doi:10.2307/1968907. JSTOR 1968907. MR 0004123. - Bestvina, Mladen; Brady, Noel (1997). "Morse theory and finiteness properties of groups".
*Inventiones Mathematicae*.**129**(3): 445–470. Bibcode:1997InMat.129..445B. doi:10.1007/s002220050168. MR 1465330. S2CID 120422255.