Whitehead’s asphericity question

Determine whether every subcomplex of an aspherical two-dimensional CW-complex is aspherical.

Background

The paper recalls Whitehead’s asphericity question for connected two-dimensional CW-complexes. Asphericity is equivalent to the vanishing of the second homotopy group, so the question asks whether an aspherical two-complex can contain a non-aspherical subcomplex. A positive answer would rule out such subcomplexes universally, while a counterexample would exhibit a subcomplex with nontrivial second homotopy inside an aspherical complex.