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.
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| - Whitehead conjecture (en)
- Whiteheads förmodan (sv)
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| - Inom matematiken är Whiteheads förmodan en förmodan gällande algebraisk topologi gjord av år 1941. Den säger att varje sammanhängande delkomplex av ett tvådimensionellt är asfäriskt. År 1997 konstruerde och en grupp G så att antingen är G ett motexempel på , eller så finns det ett motexempel på Whiteheads förmodan. (sv)
- 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. (en)
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| - 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 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. (en)
- Inom matematiken är Whiteheads förmodan en förmodan gällande algebraisk topologi gjord av år 1941. Den säger att varje sammanhängande delkomplex av ett tvådimensionellt är asfäriskt. År 1997 konstruerde och en grupp G så att antingen är G ett motexempel på , eller så finns det ett motexempel på Whiteheads förmodan. (sv)
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