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 \(C^0\)-approximate a stabilized Legendrian by a Legendrian that admits an augmentation.

中文翻译：

---

Chekanov–Eliashberg代数的持久性

我们将持续同源理论的条形码应用于Legendrian子流形的c Chekanov–Eliashberg代数，以推导任意Legendrian的位移能界。我们不要求完整的Chekanov–Eliashberg代数接受增数，因为我们仅在特定作用水平以下线性化代数。作为一个应用程序，我们表明不可能用允许增幅的Legendrian来\（C ^ 0 \） -逼近稳定的Legendrian。