Convex Embeddability and Knot Theory
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910926658076672 |
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| author | Iannella, Martina Marcone, Alberto Ros, Luca Motto Weinstein, Vadim |
| author_facet | Iannella, Martina Marcone, Alberto Ros, Luca Motto Weinstein, Vadim |
| contents | We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of circular orders. These results are then applied to the study of arcs and knots, establishing combinatorial properties and lower bounds (in terms of Borel reducibility) for the complexity of some natural relations between these geometrical objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09910 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convex Embeddability and Knot Theory Iannella, Martina Marcone, Alberto Ros, Luca Motto Weinstein, Vadim Logic Combinatorics Geometric Topology 03E15, 06A05, 57K10, 57M30 We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of circular orders. These results are then applied to the study of arcs and knots, establishing combinatorial properties and lower bounds (in terms of Borel reducibility) for the complexity of some natural relations between these geometrical objects. |
| title | Convex Embeddability and Knot Theory |
| topic | Logic Combinatorics Geometric Topology 03E15, 06A05, 57K10, 57M30 |
| url | https://arxiv.org/abs/2309.09910 |