Zeeman conjecture
In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex , the space is collapsible. It can nowadays be restated as the claim that for any 2-complex which is homotopy equivalent to a point, some barycentric subdivision of is collapsible.[1]
![{\displaystyle K\times [0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43e2fb8d4b78388febd562c9e819d1d82dedd778)
![{\displaystyle G\times [0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a60106ef8bb9b0f649b823b2b22aa7565e0b3ae7)
The conjecture, due to Christopher Zeeman, implies the Poincaré conjecture and the Andrews–Curtis conjecture.
References
- ^ Adiprasito; Benedetti (2012), Subdivisions, shellability, and the Zeeman conjecture, arXiv:1202.6606v2 Corollary 3.5
- Matveev, Sergei (2007), "1.3.4 Zeeman's Collapsing Conjecture", Algorithmic Topology and Classification of 3-Manifolds, Algorithms and Computation in Mathematics, vol. 9, Springer, pp. 46–58, ISBN 9783540458999
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