Thick braids and other non-trivial homotopy in configuration spaces of hard discs
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908852337770496 |
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| author | Ramsey, Patrick |
| author_facet | Ramsey, Patrick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16776 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Thick braids and other non-trivial homotopy in configuration spaces of hard discs Ramsey, Patrick Geometric Topology Algebraic Topology Metric Geometry 55R80 (Primary) 51F99 (Secondary) 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. |
| title | Thick braids and other non-trivial homotopy in configuration spaces of hard discs |
| topic | Geometric Topology Algebraic Topology Metric Geometry 55R80 (Primary) 51F99 (Secondary) |
| url | https://arxiv.org/abs/2311.16776 |