  We prove similar theorems concerning the structure of bundles involving
complements of fiber-type hyperplane arrangements and orbit configuration
spaces. These results facilitate analysis of the fundamental groups of these
spaces, which may be viewed as generalizations of the Artin pure braid group.
In particular, we resolve two disparate conjectures. We show that the Whitehead
group of the fundamental group of the complement of a fiber-type arrangement is
trivial, as conjectured by Aravinda, Farrell, and Rouchon. For the orbit
configuration space corresponding to the natural action of a finite cyclic
group on the punctured plane, we determine the structure of the Lie algebra
associated to the lower central series of the fundamental group. Our results
show that this Lie algebra is isomorphic to the module of primitives in the
homology of the loop space of a related orbit configuration space, as
conjectured by Xicotencatl.
