In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex K {\displaystyle K} , the space K × [ 0 , 1 ] {\displaystyle K\times [0,1]} is collapsible. It can nowadays be restated as the claim that for any 2-complex G {\displaystyle G} which is homotopy equivalent to a point, some barycentric subdivision of G × [ 0 , 1 ] {\displaystyle G\times [0,1]} is collapsible. The conjecture, due to Christopher Zeeman, implies the Poincaré conjecture and the Andrews–Curtis conjecture.
References
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