The persistence of the Chekanov–Eliashberg algebra
Georgios Dimitroglou Rizell, Michael G. Sullivan · Selecta Mathematica · 2020
Abstract We apply the barcodes of persistent homology theory to the c 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 $$C^0$$ C 0 -approximate a stabilized Legendrian by a Legendrian that admits an augmentation.