Floer homology, clasp-braids and detection results
Fraser Binns, Subhankar Dey
TL;DR
This paper extends the detection capabilities of link Floer homology to characterize links nearly braided, leading to new detection results for specific links like the Whitehead link and L7n2.
Contribution
It provides a topological characterization of almost braided links via link Floer homology, expanding detection results for various link invariants.
Findings
Link Floer homology detects the Whitehead link.
Link Floer homology detects L7n2.
Infinite families of detection results for link Floer and annular Khovanov homology.
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 , as well as infinite families of detection results for link Floer homology and annular Khovanov homology.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology