Ordering pure braid groups on closed surfaces

Abstract

We prove that the pure braid groups on closed, orientable surfaces are bi-orderable, and that the pure braid groups on closed, non-orientable surfaces have generalized torsion, thus they are not bi-orderable.

6 pages, 3 figures

References in corpus (1)

• On the fundamental group of the complement of a complex hyperplane arrangement

Cited by in corpus (4)

• Free group automorphisms, invariant orderings and topological applications
• A survey of surface braid groups and the lower algebraic K-theory of their group rings
• On presentation of Surface Braid Groups
• On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces