Year: 2025
Type: preprint
Abstract: We partially determine grid homology (combinatorial knot Floer homology) of diagonal knots, which are conjectured to be equivalent to positive braid knots, by exploiting nice grid diagrams. Its next-to-top term detects the number of prime factors, and the $\text{top}-2$ term corresponds to the decompositions of the knot into two non-integer tangles. We compare diagonal knots to various classes of knots, such as positive braids, fibered positive knots, and $L$-space knots.
Source: arXiv (Cornell University)
Author: Kubota, Hajime
Institution: Kyoto University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407212753