Dehn's lemma and the sphere theorem (Papakyriakopoulos)
Lema de Dehn y teorema de la esfera (Papakyriakopoulos)
- Date
- 1957 · confidence high
- Place
- Princeton University, New Jersey, United States
- Credited to
- Christos Papakyriakopoulos
- Field
- Knowledge & symbols
What was discovered
He proved Dehn's lemma, stated in 1910 with an error, and the loop and sphere theorems for 3-manifolds. They are the foundation of modern three-dimensional topology.
Dehn's original proof (1910) contained a gap found by Kneser in 1929. Papakyriakopoulos, a Greek, settled it at Princeton with the support of Ralph Fox; results published in Annals of Mathematics (1957).
What it led to
- Haken's and Waldhausen's theory of 3-manifolds
- Kneser-Milnor decomposition of 3-manifolds