Year: 2026
Type: preprint
Abstract: We determine the Maslov-graded next-to-top term of knot Floer homology for fibered positive links. Its rank in Maslov grading (-1) is the number of nontrivial prime connected-sum factors plus the number of components minus one, and the remaining summand is supported in Maslov grading zero. For a knot, the dimension of this remaining summand is determined by its Alexander polynomial. The proof combines a preferred-crossing construction with reductions of generalized Seifert surfaces to planar pretzel surfaces and a graded skein induction. We also obtain bounds on the fixed points of monodromies for fibered positive knots.
Source: arXiv (Cornell University)
Author: Cheng, Zhechi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221832172