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 ${\displaystyle G}$ which is homotopy equivalent to a point, some barycentric subdivision of ${\displaystyle G\times [0,1]}$ is collapsible.^[1]

The conjecture, due to Christopher Zeeman, implies the Poincaré conjecture and the Andrews–Curtis conjecture.

References

1. 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