The knot Floer homology and embedded contact homology correspondence conjecture
The knot Floer homology and embedded contact homology correspondence conjecture
Let be a null-homologous knot of genus . Let be the complement of an open tubular neighbourhood of , and let be a contact form on for which is a negative Morse-Bott torus foliated by meridians of . For each integer , let denote the homology of the subcomplex of generated by orbit sets in with total linking number with .
ECH–knot Floer correspondence conjecture. There is an isomorphism
This conjecture is obtained by combining the preceding sutured ECH–SFH conjecture with a theorem relating the relevant ECH groups and the relation between sutured Floer homology and knot Floer homology. Its resolution is not specified in the source.
Sources & referencesView supporting material
Primary source
Paolo Ghiggini, Vincent Colin and Ko Honda, “An exposition of the equivalence of Heegaard Floer homology and embedded contact homology”, arXiv:2004.09626 (2020).
Additional references
2 papers in this index state this conjecture (2006–2020). The statement above is taken from the most recent of them; the others are arXiv:math/0601443.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.