Whitehead conjecture

The Whitehead conjecture (also known as the Whitehead asphericity conjecture) is a claim in algebraic topology.It states that every connected subcomplex of a two-dimensional aspherical CW complex is aspherical.is called aspherical if the two-dimensional CW complexThe 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 theoremWhitehead problemalgebraic topologyJ. H. C. WhiteheadconnectedasphericalCW complexgroup presentationMladen BestvinaEilenberg–Ganea conjectureWhitehead, J. H. C.Annals of MathematicsBestvina, MladenInventiones MathematicaeBibcodetopology-related