Knot primality: knot Floer homology, metacyclic representations and twisted homology
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909732601593856 |
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| author | Allen, Samantha Livingston, Charles |
| author_facet | Allen, Samantha Livingston, Charles |
| contents | We develop purely algebraic methods for proving that a knot is prime. Our approach uses the Heegaard Floer polynomial in conjunction with classical knot-theoretic methods: cyclic, dihedral, and metacyclic covering spaces. The theory of twisted homology allows us to view these approaches from a unified perspective. Collectively, the primality tests developed here have proved primality for over 99.6% of knots in large families of prime knots, including all prime knots with 15 or fewer crossings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knot primality: knot Floer homology, metacyclic representations and twisted homology Allen, Samantha Livingston, Charles Geometric Topology We develop purely algebraic methods for proving that a knot is prime. Our approach uses the Heegaard Floer polynomial in conjunction with classical knot-theoretic methods: cyclic, dihedral, and metacyclic covering spaces. The theory of twisted homology allows us to view these approaches from a unified perspective. Collectively, the primality tests developed here have proved primality for over 99.6% of knots in large families of prime knots, including all prime knots with 15 or fewer crossings. |
| title | Knot primality: knot Floer homology, metacyclic representations and twisted homology |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.08102 |