The second term in knot Floer homology

It is well known that the genus g of a knot is the highest Alexander grading for which the knot Floer homology is nontrivial. In recent years, there is evidence suggesting that the knot Floer homology is also nontrivial in the Alexander grading g-1. In this talk, I will describe a proof that the rank of the second-to-top term of the knot Floer homology is greater than or equal to the rank of the topmost term when the topmost term is supported in a single Maslov grading.

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