The next-to-top term of the knot Floer homology of some non-fibered knots

2026/08/04 by Fraser Binns, Shunyu Wan
Mathematics · #math.GT #msc:57K18

paper · pdf

29 pages, 8 figures, comments welcome

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

Sivek conjectured that the rank of knot Floer homology in the next-to-top Alexander grading is at least the rank in the top Alexander grading. Baldwin and Vela-Vick verified this conjecture in the case of fibered knots arXiv:1801.06563. Ni gave a generalization of this result (for knots in generalized L-spaces) to cases in which the knot Floer homology satisfies an algebraic condition arXiv:2104.14687. We give an independent generalization of Baldwin and Vela-Vick's result to a family of knots with Seifert surfaces satisfying certain conditions.

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