Zeeman conjecture

In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex ${\displaystyle K}$, the space ${\displaystyle K\times [0,1]}$ is collapsible. It can nowadays be restated as the claim that for any 2-complex G which is homotopic to a point, there is an interval I such that some barycentric subdivision of G × I is contractible.^[1]

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