Open Collections

Description

Let \(F_k(M)\) denote the ordered k-point configuration space of a connected open manifold M. For a given manifold, as \(k\) increases, this family of spaces exhibits a phenomenon called "representation stability" with respect to the natural symmetric group actions. In this talk I will discuss what this means and describe a new method for establishing this form of stability, extending previous results of Church and others to include non-orientable manifolds. This project is work in progress, joint with Jeremy Miller.