The persistence of the Chekanov-Eliashberg algebra
Georgios Dimitroglou Rizell, Michael G. Sullivan
TL;DR
This paper introduces a novel application of persistent homology barcodes to the Chekanov-Eliashberg algebra, providing new bounds on Legendrian displacement energy without requiring augmentations.
Contribution
It extends the use of persistent homology to analyze Legendrian invariants and establishes non-approximability results for stabilized Legendrians by augmentable Legendrians.
Findings
Displacement energy bounds derived for Legendrians.
Non-approximability of stabilized Legendrians by augmentable ones.
Application of persistent homology to Legendrian contact homology.
Abstract
We apply the barcodes of persistent homology theory to the Chekanov-Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. We do not require the full Chekanov-Eliashberg algebra to admit an augmentation as we linearize the algebra only below a certain action level. As an application we show that it is not possible to -approximate a stabilized Legendrian by a Legendrian that admits an augmentation.
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.