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

Patrick Ramsey

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arXiv · 2311.16776

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

Patrick Ramsey

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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.

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Patrick Ramsey. 2023-11-28. Thick braids and other non-trivial homotopy in configuration spaces of hard discs. https://arxiv.org/abs/2311.16776

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