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The persistence of the Chekanov-Eliashberg algebra (1810.10473v2)
Published 24 Oct 2018 in math.SG and math.GT
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 $C0$-approximate a stabilized Legendrian by a Legendrian that admits an augmentation.
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