A rank-minimality condition in sutured Heegaard Floer homology forces a connect-sum decomposition with a Floer simple knot, and link Floer homology detects spherical braid closures in S^1×S^2.
Floer homology, clasp-braids and detection results
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Martin showed that link Floer homology detects braid axes. In this paper we extend this result to give a topological characterisation of links which are almost braided from the point of view of link Floer homology. The result is inspired by work of Baldwin-Sivek and Li-Ye on nearly fibered knots. Applications include that Khovanov homology detects the Whitehead link and $L7n2$, as well as infinite families of detection results for link Floer homology and annular Khovanov homology.
citation-role summary
method 1
citation-polarity summary
fields
math.GT 1years
2025 1verdicts
CONDITIONAL 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
On Heegaard Floer minimal knots in sutured manifolds
A rank-minimality condition in sutured Heegaard Floer homology forces a connect-sum decomposition with a Floer simple knot, and link Floer homology detects spherical braid closures in S^1×S^2.