On topological properties of configuration spaces ofcertain specialized graphs

The purpose of this thesis is to study the space of all positions of k distinct particles on a graph, where the particles are not allowed to collide. The configuration space of ordered k-tuples has been studied extensively when X is known to be a manifold. Less is known for singular spaces, such as graphs. These spaces have arisen recently in robotics and physics and are interesting to study in their own right. We study the k-configuration spaces of certain types of graphs Γ where k > 2 and calculate the homology of Conf(Γ, 3) using a natural cover and the Mayer-Vietoris spectral sequence. The concept of an “information bundle” will be defined and we will calculate the order of information bundles of planar and non-planar graphs. Results for stable splittings are discussed.