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arXiv · 1810.10473

The persistence of the Chekanov-Eliashberg algebra

Georgios Dimitroglou Rizell·Michael G. Sullivan
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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 $C^0$-approximate a stabilized Legendrian by a Legendrian that admits an augmentation.

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Georgios Dimitroglou Rizell, Michael G. Sullivan. 2018-10-24. The persistence of the Chekanov-Eliashberg algebra. https://arxiv.org/abs/1810.10473

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