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Whitehead conjecture : ウィキペディア英語版
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==

* () J. H. C. Whitehead, ''On adding relations to homotopy groups'', Annals of Mathematics, 2nd Ser., 42 (1941), no. 2, 409 –428.
*() Mladen Bestvina, Noel Brady, ''Morse theory and finiteness properties of groups'', Inventiones Mathematicae 129 (1997), no. 3, 445 – 470.


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