1. References

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.

References

• {{Cite journal| last=Whitehead|first=J. H. C.|authorlink= J. H. C. Whitehead| title=On adding relations to homotopy groups|journal=Annals of Mathematics|series=2nd Ser. | volume=42|year=1941|issue=2|pages=409–428|doi=10.2307/1968907|mr=0004123}}
• {{Cite journal| last1= Bestvina|first1=Mladen|authorlink1=Mladen Bestvina|last2=Brady|first2=Noel|title=Morse theory and finiteness properties of groups|journal= Inventiones Mathematicae|volume= 129 |year=1997|issue=3|pages=445–470|doi=10.1007/s002220050168|mr=1465330}}

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