The persistence of the Chekanov–Eliashberg algebra

• Georgios Dimitroglou Rizell ^[1] ; Michael G. Sullivan ^[2]
  1. [1] Uppsala University

     Uppsala University

     Uppsala domkyrkoförs., Suecia

     
  2. [2] University of Massachusetts System

     University of Massachusetts System

     City of Boston, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 5, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00598-y
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• Resumen

  • 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 C0-approximate a stabilized Legendrian by a Legendrian that admits an augmentation.