TL;DR
This paper constructs a CW-spectrum refinement of Bar-Natan homology for links, providing a stable homotopy type invariant and proposing a conjecture about lifting the quantum filtration to a cohomotopical level.
Contribution
It introduces a spatial refinement of Bar-Natan homology as a CW-spectrum, establishing a new link invariant and conjecturing a lift of the quantum filtration.
Findings
Constructed CW-spectrum $\
Proved the stable homotopy type is a link invariant
Conjectured a lift of the quantum filtration to the spatial level
Abstract
A spatial refinement of Bar-Natan homology is given, that is, for any link diagram we construct a CW-spectrum whose reduced cellular cochain complex gives the Bar-Natan complex of . The stable homotopy type of is a link invariant and is described as the wedge sum of the canonical cells. We conjecture that the quantum filtration of Bar-Natan homology also lifts to the spatial level, and that it leads us to a cohomotopical refinement of the -invariant.
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.