On 2-dimensional aspherical complexes and a problem of J. H. C. Whitehead

Abstract

In [W] J. H. C. Whitehead posed the following question: ‘Is every subcomplex K of a 2-dimensional aspherical complex L itself aspherical ?’This problem is usually referred to as the ‘Whitehead Conjecture’ though it was only stated in the form of a question. For convenience we treat it also as a conjecture.The Whitehead Conjecture has been proved in special cases: if the subcomplex K has only one 2-cell, and also in the case where π1(K) is either finite, abelian, of free [C] For more partial results see, for example, the introduction of [H1].