The persistence of the Chekanov-Eliashberg algebra
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.
Keywords
Cite
@article{arxiv.1810.10473,
title = {The persistence of the Chekanov-Eliashberg algebra},
author = {Georgios Dimitroglou Rizell and Michael G. Sullivan},
journal= {arXiv preprint arXiv:1810.10473},
year = {2020}
}
Comments
29 pages, 4 figures; version accepted for publication in Selecta Mathematica. This is a major revision with many fixes and improvements. The constant in Theorem 1.1 has been improved. The theory of barcodes have been properly introduced in the new Section 2 together with new related terminology. The proof of Theorem 1.1 was rewritten in the new language and given a greater level of details