Whitehead conjecture

Whitehead conjecture

The Whitehead 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.

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.

References

* [http://links.jstor.org/sici?sici=0003-486X%28194104%292%3A42%3A2%3C409%3AOARTHG%3E2.0.CO%3B2-5] J. H. C. Whitehead, "On adding relations to homotopy groups", Annals of Mathematics, 2nd Ser., 42 (1941), no. 2, 409 –428.

* [http://www.springerlink.com/content/nhj24dgb0vb7bx5p/?p=3b9c54d35a7c445587b1fc97576a6a83&pi=1] Mladen Bestvina, Noel Brady, "Morse theory and finiteness properties of groups", Inventiones Mathematicae 129 (1997), no. 3, 445 – 470.


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