Abstract
We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 107-113 |
| Number of pages | 7 |
| Journal | Geometriae Dedicata |
| Volume | 147 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2010 |
| Externally published | Yes |
Keywords
- Free group
- Mapping class group
- Pure braid group
ASJC Scopus subject areas
- Geometry and Topology