Parametrized topological complexity of hyperplane arrangement bundles

The parametrized approach to motion planning offers flexibility for variable situations, typically encoded in a fiber bundle with the base space parametrizing external constraints on the system. Here, the input (initial and terminal states) and the output (a path between them) of a motion planning algorithm must all be subject to the same external conditions (that is, they are in the same fiber of the bundle). We consider this parametrized motion planning problem where each of the spaces involved is the complement of a union of hyperplanes in a complex vector space. Under a combinatorial hypothesis of supersolvability, we determine the parametrized topological complexity of a fiber bundle of arrangement complements. This is joint work with Dan Cohen.