Two-generator subgroups of the pure braid group

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.

7 pages

Cited by in corpus (1)

• Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents