Concordances of sums of alternating torus knots and their mirrors to $L$-space knots
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917593620676608 |
|---|---|
| author | Guyer, Dan Sachen, Thomas |
| author_facet | Guyer, Dan Sachen, Thomas |
| contents | Continuing the work of Zemke, Livingston and Allen, we consider when linear combinations of torus knots are concordant to $L$-space knots. We begin by proving Allen's conjecture for alternating torus knots. That is, we prove that a linear combination of alternating torus knots is concordant to an $L$-space knot if and only if the connected sum is a single torus knot. Then we establish a necessary condition for when a linear combination of torus knots is concordant to an $L$-space knot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08055 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Concordances of sums of alternating torus knots and their mirrors to $L$-space knots Guyer, Dan Sachen, Thomas Geometric Topology Algebraic Topology Primary: 57N70, 57M12 Secondary: 57K10 Continuing the work of Zemke, Livingston and Allen, we consider when linear combinations of torus knots are concordant to $L$-space knots. We begin by proving Allen's conjecture for alternating torus knots. That is, we prove that a linear combination of alternating torus knots is concordant to an $L$-space knot if and only if the connected sum is a single torus knot. Then we establish a necessary condition for when a linear combination of torus knots is concordant to an $L$-space knot. |
| title | Concordances of sums of alternating torus knots and their mirrors to $L$-space knots |
| topic | Geometric Topology Algebraic Topology Primary: 57N70, 57M12 Secondary: 57K10 |
| url | https://arxiv.org/abs/2210.08055 |