// Workers AI · dad joke modeWhat did Zeeman conjecture at the party? A splitting headache.

In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex $K$, the space $K\times [0,1]$ is collapsible. It can nowadays be restated as the claim that for any 2-complex $G$ which is homotopy equivalent to a point, some barycentric subdivision of $G\times [0,1]$ 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