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

2023/11/28 by Patrick S. Ramsey, Ramsey, Patrick
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2311.16776

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 π_n-3 for all n. We also explore the persistence of these nontrivial classes when the ambient disc is deformed into an ellipse.

Related

• Configuration spaces of disks in an infinite strip
• Representation Stability for Disks in a Strip
• Topological embeddings of disks via configuration categories
• Higher-categorical combinatorics of configuration spaces of Euclidean space
• Configuration spaces of an embedding torus and cubical spaces