Thick braids and other non-trivial homotopy in configuration spaces of hard discs

Abstract

We study ordered configuration spaces of $n$ hard discs inside a unit disc, and how the topology changes with the radius $r$ of the hard discs. We describe the full homotopy type of this space for all radii when $n = 4$ and exhibit nontrivial classes in $\pi_{n-3}$ for all $n$. We also explore the persistence of these nontrivial classes when the ambient disc is deformed into an ellipse.