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Conjecture

Whitehead Conjecture

Geometry

The Whitehead conjecture, also known as the Whitehead asphericity conjecture, is a claim in algebraic topology formulated by J. H. C. Whitehead in 1941. It states that every connected subcomplex of a two-dimensional aspherical CW complex is itself aspherical. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Statement
Every connected subcomplex of a two-dimensional aspherical CW complex is aspherical. 1
Proposed Year
1941 1
Progress Toward Resolution
In 1997 Bestvina and Brady showed that the Whitehead and Eilenberg-Ganea conjectures cannot both be true. 1
Classification
Resolution Status
Open 1
Prize Status
Prize Status (category)
No Prize Offered 1
Connections

In Branch

Algebraic Topology, Branches of Mathematics
Source Whitehead Conjecture (Wikipedia)
Sources
1. Whitehead Conjecture (Wikipedia)
Wikimedia Foundation
  • Lead section
    It was formulated by J. H. C. Whitehead in 1941.
  • Lead section, second sentence
    every connected subcomplex of a two-dimensional aspherical CW complex is aspherical
  • Lead section, last sentence
    it is not possible for both conjectures to be true
  • In Branch: Algebraic Topology, Lead sentence
    e Whitehead asphericity conjecture) is a claim in algebraic topology.
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