Orbifold braid groups

Abstract

The orbifold braid groups of two dimensional orbifolds were defined in [1] (arXiv:math/9907194) to understand certain Artin groups as subgroups of some suitable orbifold braid groups. We studied orbifold braid groups in some more detail in [17] (arXiv:2006.07106) and [18] (arXiv:2106.08110), to prove the Farrell-Jones Isomorphism conjecture for orbifold braid groups and as a consequence for some Artin groups. In this article we apply the results from [17] and [18], to study two aspects of the orbifold braid groups. First we show that the homomorphisms induced on the orbifold braid groups by the inclusion maps of a generic class of sub-orbifolds of an orbifold are injective. Then, we prove that the centers of most of the orbifold braid groups are trivial.