TL;DR
This paper proves that certain alternating diagrams of quasipositive links are necessarily positive, leading to the conclusion that such links are strongly quasipositive, which advances understanding of their structure.
Contribution
It establishes a new condition under which alternating quasipositive links are shown to be positive and strongly quasipositive, linking diagram properties to link classification.
Findings
Alternating quasipositive links with specific Seifert circle conditions are positive.
Such links are necessarily strongly quasipositive.
The result connects diagram properties with algebraic link properties.
Abstract
We prove that if a quasipositive link can be represented by an alternating diagram satisfying the condition that no pair of Seifert circles is connected by a single crossing, then the diagram is positive and the link is strongly quasipositive.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.