Misplaced Pages

In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex ${\displaystyle K}$, the space ${\displaystyle K\times }$ is collapsible. It which 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.

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

This topology-related article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e

1. Adiprasito; Benedetti (2012), Subdivisions, shellability, and the Zeeman conjecture, arXiv:1202.6606v2 Corollary 3.5

• Conjectures
• Unsolved problems in geometry
• Geometric topology
• Topology stubs