# On the geography and botany of knot Floer homology

@article{Hedden2014OnTG,
title={On the geography and botany of knot Floer homology},
author={Matthew Hedden and Liam Watson},
journal={Selecta Mathematica},
year={2014},
volume={24},
pages={997-1037}
}
• Published 28 April 2014
• Mathematics
• Selecta Mathematica
This paper explores two questions: (1) Which bigraded groups arise as the knot Floer homology of a knot in the three-sphere? (2) Given a knot, how many distinct knots share its Floer homology? Regarding the first, we show there exist bigraded groups satisfying all previously known constraints of knot Floer homology which do not arise as the invariant of a knot. This leads to a new constraint for knots admitting lens space surgeries, as well as a proof that the rank of knot Floer homology…

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