Finding Topology in a Factory: Configuration Spaces

The examples of topological spaces that we construct in this exposition arose simultaneously from two seemingly disparate fields: the first author, in his thesis [1], discovered these spaces after working with H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow on problems about random walks on graphs [2]. The second author discovered these same spaces while collaborating with D. Koditschek in the Artificial Intelligence Lab at the University of Michigan; see [7] and [8].