The Whitehead conjecture is a claim in algebraic topology

Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...

. It was formulated by J. H. C. Whitehead

J. H. C. Whitehead

John Henry Constantine Whitehead FRS , known as Henry, was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai , in India, and died in Princeton, New Jersey, in 1960....

 in 1941. It states that every connected

Connectedness

In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected...

 subcomplex of a two-dimensional aspherical

Aspherical space

In topology, a branch of mathematics, an aspherical space is a topological space with all higher homotopy groups equal to 0.If one works with CW complexes, one can reformulate this condition: an aspherical CW complex is a CW complex whose universal cover is contractible. Indeed, contractibility of...

 CW complex

CW complex

In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial naturethat allows for...

 is aspherical.

In 1997, Mladen Bestvina

Mladen Bestvina

Mladen Bestvina is a Croatian American mathematician working in the area of geometric group theory. He is a Distinguished Professor in the Department of Mathematics at the University of Utah.-Biographical info:...

 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.