An Exceptional Collection For Khovanov Homology
Benjamin Cooper, Matt Hogancamp
TL;DR
This paper constructs chain complexes related to the Temperley-Lieb algebra to advance the understanding of Khovanov homology, leading to new decompositions and structural insights in categorification.
Contribution
It introduces a novel construction of chain complexes for minimal idempotents in the Temperley-Lieb algebra, impacting Khovanov homology and its categorifications.
Findings
Semi-orthogonal decompositions of categorified Temperley-Lieb algebras
Postnikov decompositions of Khovanov tangle invariants
Enhanced structural understanding of Khovanov homology
Abstract
The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which determines Khovanov homology. Consequences of our work include semi-orthogonal decompositions of categorifications of Temperley-Lieb algebras and Postnikov decompositions of all Khovanov tangle invariants.
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.