Title: Topological Complexity and Graphic Hyperplane Arrangements.

Abstract: A motion planning algorithm for a topological space X is a (possibly not continuous) assignment of paths to ordered pairs of points in X. The topological complexity of X is an integer invariant which measures the extent to which any motion planning algorithm for X must be discontinuous. In practice it is difficult to compute, but it is bounded below by an integer invariant of the cohomology ring of X, called the zero-divisors-cup-length of X. When X is the complement of an arrangement of hyperplanes, this ring is the Orlik-Solomon algebra of A and the lower bound can be controlled by some combinatorial conditions. When X is the complement of a graphic arrangement, there is a connection between topological complexity and a classical result in graph theory, the Nash-Williams decomposition theorem.