Baker's Floer-simple knot conjecture
Let be a lens space and let be a knot. A knot is Floer simple when its Floer-theoretic complexity is minimal, and it is simple when it belongs to the standard class of simple knots in a lens space. Baker's Floer-simple knot conjecture. If is Floer simple, then is simple. This is a Floer-theoretic formulation of the Berge conjecture and is related to slope detection through the characterization of Floer simplicity by non-NLS-detection of the knot meridian. Its general validity remains open.
References
Primary source
Qingfeng Lyu, “The knot meridians of (1,1)-knot complements are CTF-detected”, arXiv:2410.20013 (2025).
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