Floer homology and non-fibered knot detection
Abstract
We prove that knot Floer homology and Khovanov homology can detect non-fibered knots, including the knot $5_2$, and that HOMFLY homology detects infinitely many such knots. This is the first time that a Floer theory or any of the Khovanov-Rozansky link homology theories has been shown to detect non-fibered knots, or infinitely many knots. These results rely on our main theorem, which gives a complete classification of genus-1 knots in $S^3$ whose knot Floer homology in the top Alexander grading is 2-dimensional.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.03307
- arXiv:
- arXiv:2208.03307
- Bibcode:
- 2022arXiv220803307B
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Quantum Algebra
- E-Print:
- 65 pages, 30 figures