Research demonstrates chain homotopy types of knot floer complexes in knots of width 2, implying all montesinos knots can be simplified.
This paper classifies the chain homotopy equivalence types of knot Floer complexes {CFK}F[U,V](K) of knot Floer width 2 . They have no nontrivial local systems. As an application, this shows that all Montesinos knots admit a basis that can be simultaneously horizontally and vertically simplified.
No takes yet. Share an insight, caveat, or question.
David Popović (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: