Legendrian knots and multi-crossings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909195114119168 |
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| author | Kumar, Amit Murphy, Jake Naff, Brian |
| author_facet | Kumar, Amit Murphy, Jake Naff, Brian |
| contents | It was shown in arXiv:1208.5742 that any smooth knot can be represented by an übercrossing projection, i.e. a knot projection with no crossings aside from a single multi-crossing. We extend this idea to Legendrian knots and investigate übercrossing and petal projections in the front and Lagrangian projections. We show that any Legendrian knot with an übercrossing projection in the front projection is smoothly isotopic to the unknot and we demonstrate how to compute the $tb$ and rotation numbers for petal projections in the Lagrangian projection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Legendrian knots and multi-crossings Kumar, Amit Murphy, Jake Naff, Brian Geometric Topology 57M27, 53D10 It was shown in arXiv:1208.5742 that any smooth knot can be represented by an übercrossing projection, i.e. a knot projection with no crossings aside from a single multi-crossing. We extend this idea to Legendrian knots and investigate übercrossing and petal projections in the front and Lagrangian projections. We show that any Legendrian knot with an übercrossing projection in the front projection is smoothly isotopic to the unknot and we demonstrate how to compute the $tb$ and rotation numbers for petal projections in the Lagrangian projection. |
| title | Legendrian knots and multi-crossings |
| topic | Geometric Topology 57M27, 53D10 |
| url | https://arxiv.org/abs/2405.04724 |