Categorified Wrapping Number Conjecture
For every annular link , the annular Khovanov homology of is nonzero in the -grading equal to the wrapping number of : .
References
Primary source
Additional references
- Categorified Wrapping Number Conjecture — Journal of Knot Theory and Its Ramifications — Benjamin Daniels, Melissa Zhang
Progress summary
A 2025 theorem proves the conjecture for broad families of annular links, but no proof for every annular link has been reported.
Eli Grigsby posed the conjecture at MSRI in 2010: every annular link should have nonzero annular Khovanov homology in grading .
Known results
- Daniels–Zhang (2025): the conjecture holds when a diagram has a perfectly wrapped, uniform resolution.
- This includes adequately wrapped annular links and, in particular, alternating annular links.
- Further cases include certain annular closures of tangles with plumbed-link phenomena.
January 2025 theorem; August 2026 publication
Benjamin Daniels and Melissa Zhang’s paper establishes these broad cases, but explicitly leaves open whether every annular link admits the required resolution. Thus it is substantial progress, not a universal solution.
Current status (as of August 2026): The conjecture is settled for alternating links and other broad families, while the case of all annular links remains open.
Sources
- arxiv.org
- ar5iv.labs.arxiv.org
- doi.org
- math.ucdavis.edu
- ar5iv.labs.arxiv.org
- arxiv.org
- meetings.ams.org
- mathoverflow.net
- quantamagazine.org
- deepmind.google
- quantamagazine.org
- quantamagazine.org
- quantamagazine.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- quantamagazine.org
- quantamagazine.org
Solutions 0
No solutions have been posted yet.